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Research on Interactions of Algebraic Geometry, Hodge Theory and Logarithmic Geometry

Research Project

Project/Area Number 11304001
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka University

Principal Investigator

USUI Sampei  Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90117002)

Co-Investigator(Kenkyū-buntansha) MUKAI Shigeru  Kyoto University, Research Institute of Math. Sci., Professor, 数理解析研究所, 教授 (80115641)
KATO Kazuya  Kyoto University, Grad. Sch. of Sci., Professor, 大学院・理学研究科, 教授 (90111450)
NAKAMURA Iku  Hokkaido University, Grad. Sch. of Sci., Professor, 大学院・理学研究科, 教授 (50022687)
KONNO Kazuhiro  Osaka University, Grad. Sch. of Sci., Associate Professor, 大学院・理学研究科, 助教授 (10186869)
MORI Shigefumi  Kyoto University, Research Institute of Math. Sci., Professor, 数理解析研究所, 教授 (00093328)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥25,910,000 (Direct Cost: ¥23,900,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2001: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2000: ¥9,900,000 (Direct Cost: ¥9,900,000)
Fiscal Year 1999: ¥7,300,000 (Direct Cost: ¥7,300,000)
KeywordsLogarithmic Hodge Theory / Compactifications of Moduli / Invariant Functions / Torelli Problem / Algebraic Varieties / Canonical Rings / Vector Bundles / Symplectic Varieties / 標準束公式 / 2次包 / 特異シンプレクティック多様体 / Log Hodge構造 / 退化 / 周期写像 / 一般型多様体 / symplectic多様体 / 有理端曲線
Research Abstract

The main symposia held during the preiod :
1) "Algebraic Geometry and Topology of Degenerations, Coverings and Singularities", February, 2000, Tohoku Gakuin University. Organizing Committee : T. Ashikaga, S. Ogata, K. Konno. There were interactions among verious branches.
2) World Symposium "Algebraic Geometry 2000, Azumino", July 2000, Nagano. Organizing Committee : M. Green, L. Illusie, K. Kato, E. Looijenga, S. Mukai, S. Saito, S. Usui (Chief). There were 150 pRticitants, including 60 from out-side Japan, who enjoied stimulating discussions. The principal event of this project was successful.
3) World Symposium "Algebraic Geometry in East Asia", August 2001, International Institute for Advanced Studies, Kyoto. Organizing Committee : K. Konno, A. Moriwaki, N. Nakayama, A. Ohbuchi (Chief), S. Usui. There were about 60 prticitants, including 15 from countries out-side Japan mainly in east Asia, who enjoied Stimulating discussions. This symposium will be probably continuously held in coutries in east Asia.
4) "Algebraic Geometry Symposium", Kinosaki, Hyogo. This is the biggest annual symposium on Algebraic Geometry in Japan. November 1999, Organizing Committee : K. Konno, T. Usa. Ocober 2000, Organizing Committee : F. Kato, K. Ohno. October 2001, Organizing Committee : M. Kobayashi, H. Tokunaga.
5) "Hodge athory and Algebraic Geometry". This is an annual symposium which continues almost 20 years. Ocober 1999, Kagoshima University, Organizing Committee : M. Asakura, S. Tsuboi, S. Usui. November 2001, Osaka University, Organizing Committee : M. Asakura, S. Saito, I. Satake, S. Usui.
The main result of individual reaesrches is a construction of fine moduli of logarithmic Hodge Structures by K. Kato and S. Usui. The other reserch results by the members of this project are found in the list of references on the next pages.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (175 results)

All Other

All Publications (175 results)

  • [Publications] Usui, S., Kato, K.: "Logarithmic Hodge structures and their moduli"(Preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S., Kato, K.: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math. : Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S.: "Recovery of vanishing cycles by log geometry"Tohoku Math. J.. 53-1. 1-36 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S.: "Torelli type problems"Sugaku Expositions, Amer. Math. Soc.. 13. 17-38 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S., Kato, K.: "Logarithmic Hodge structures and classifying spaces(summary)"The arithmetic and geometry of algebraic cycles (Banff, Canada, 1998), CRM Proc. Lecture Notes. 24. 115-130 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S.: "Recovery of vanishing cycles by log geometry : Case of several variables"Proceeding of International Conference "Commutative Algebra and Algebraic Geometry and Computational Methods", Hanoi 1996, Springer-Verlag. 135-144 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] 向井茂: "Verlinde公式の幾何学"数理解析研究所講究録 「組合せ論的表現論をめぐる話題,2000年10月」. (投稿予定).

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] 向井茂: "曲線と「曲面」をめぐって(数学の未解決問題♯17)"数理科学,サイエンス社. 1月号. 56-64 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K., Usui, S.: "Logarithmic Hodge structures and their moduli"(Preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K., Usui, S.: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math. : Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K., Matsubara, T., Nakayama, C.: "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math. : Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K., Usui, S.: "Logarithmic Hodge structures and classifying spaces(summary)"The arithmetic and geometry of algebraic cycles (Banff, Canada, 1998), CRM Proc. Lecture Notes. 24. 115-130 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K.: "Generalized explicit reciprocity laws"Algebraic number theory(Hapcheon/Saga, 1996), Adv. Stud. Contemp. Math. (Pusan). 1. 57-126 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "On the quadric hull of a canonical surface"(Preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K., Ashikaga, T.: "Local and global properties of pencils of algebraic curves"(Preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "1-2-3 theorem for curves on algebraic surfaces"J. reine angew. Math.. 533. 171-205 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "Certain algebraic surfaces with non-reduced moduli space"Portugal. J. Math.. 57. 169-178 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K., Margarida Mendes Lopes: "On a question of Miles Reid"manuscripta math.. 100. 81-86 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E., Kachi, Y.: "Segre's refiexivity and an inductive characterization of hyperquadrics"Memoirs of A.M.S.. (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E., Zhao Yocai: "Smooth 4-folds which contains a P^1-bundle as an ample divisor"Manuscripta math.. 101. 313-323 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E.: "Bahavior of rational curves with the minimal degree in projective space bundle in any characteristic"J. Math. Kyoto Univ.. 40-4. 673-704 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E., Kachi, Y.: "Polarized varieties whose points are joined by rational curves of small degrees"Illinois J. Math.. 43-2. 350-390 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E., Kachi, Y.: "Characterization of projective spaces and hyperquadrics"Proc. of Algebra Cconference in memory of Kurosh, Moscow 1998, Walter de Gruyler, Berlin. (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Mori, S.: "On a hyperplane section theorem of Gurjar"Math. Ann.. 319. 533-537 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Mori, S.: "Rational curves on algebraic varieties"Mathematics : Frontier and Perspectives(ed. by V.Arnold, M.Atiyah, P.Lax, and B.Mazur). 189-195 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Mori, S., Fujino, O.: "A canonical bundle formula"J. Diff. Geom.. 56. 167-188 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Sumihiro, H., Tagami, S.: "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math. J.. 31. 51-57 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Sumihiro, H.: "Determinantal varieties associated to rank two vector bundles on projective spaces and splitting theorems"Hiroshima Math. J.. 29. 371-434 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math. : Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Higher normal functions and Griffiths groups"J. of Algebraic Geometry. (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Motives, Algebraic Cycles and Hodge theory"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, CRM Proceedings and Lecture, A.M.S. 24. 235-253 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Motives and Filtrations on Chow groups, II"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, NATO Science Series, Kluwer Academic Publishers. 548. 321-346 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "The Arithmetic and Geometry of Algebraic Cycles"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, CRM Proceedings and Lecture, A.M.S. 24. (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "A compactification of the moduli scheme of abelian varieties"mathAG/0107158. (e-print).

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Plane cubic curves-from Hesse to Mumford"Sugaku,岩波書店. 53. 241-258 (2001)

    • Description
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Hilbert schemes of abelian group orbits"J. Algebraic Geometry. 10. 757-779 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I., Terasoma, T.: "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proc. of Texel conference 1999, Progress in Math., Birkhauser. 195. 299-324 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I., Gomi, Y., Shinoda, K.: "Hilbert schemes of G-orbits in dimension three"Kodaira's issue, Asian J. Math.. 4. 51-70 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Stability of degenerate abelian varieties"Invent. Math.. 136. 659-715 (1999)

    • Description
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I., Ito, Y.: "Hilbert schemes and simple singularities"New trends in algebraic goemetry, Proc. European Math. Conference 1996, London Math. Soc., Lecture Note Series, Cambridge university press. 264. 151-233 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Nakamura, I., Alexeev, V.: "On Mumford's construction of degenerating abelian varieties"Tohoku Math. J.. 51. 399-420 (1999)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Counter-example to global Torelli problem for irreducible symplectic manifolds"(preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "A note on symplectic singularities"(preprint).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International J, Math.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Deformation theory of Calabi-Yaus"Sugaku Exposition, A.M.S.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Stratified local moduli of Calabi-Yau threefolds"Topology. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Extension of 2-forms and symplectic varieties"J. Reine Angew. Math.. 539. 123-147 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Deformation theory of singular symplectic n-folds"Math. Ann.. 319. 597-623 (2001)

    • Description
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      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Global smoothing of Calabi-Yau threefolds II"Compositio Math.. 125. 55-68 (2001)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] 向井 茂: "モジュライ理論I. II.現代数学の展開#13,14(青本和彦等編)"岩波書店. xiv+175,xi+280 (1998,2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] 石田 正典: "代数幾何学の基礎"培風館. 232 (2000)

    • Description
      「研究成果報告書概要(和文)」より
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      2001 Final Research Report Summary
  • [Publications] 石田 正典: "トーリック多様体入門(すうがくの風景2)"朝倉書店. 155 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S. (with Kato. K.): "Logarithmic Hodge structures and their moduli"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S. (with Kato. K.): "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S.: "Recovery of vanishing cycles by log geometry"Tohoku Math. J.. 53-1. 1-36 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, s.: "Torelli type problems"Sugaku Expositions, Amer. Math. Soc.. 13. 17-38 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S. (with Kato. K.): "Logarithmic Hodge structures and classifying spaces (summary)"The arithmetic and geometry of algebraic cycles (Banff, Canada, 1998), CRM Proc. Lecture Notes. 24. 115-130 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Usui, S.: "Recovery of Vanishing cycles by log geometry : Case of several variables"Proceeding of International Conference "Commutative Algebra and algebraic Geometry and Computational Methods", Hanoi 1996, Springer-Verlag. 135-144 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mukai, S.: "Geometry of Velinde's formula (in Japanese)"Lecture Note of RIMS, Kyoto Univ., "Topics in Combinatoric Representation Theory, Oct., 2000". (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
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      2001 Final Research Report Summary
  • [Publications] Mukai, S.: "On curves and "Surfaces" (Open Problems in Mathematics #17)"Suri-Kagaku, Science-Sha. January. 56-64 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K. (with Usui, S.): "Logarithmic Hodge structures and their moduli"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K. (with Usui, S.): "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math. Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K. (with Matsubara, T. and Nakayama, C.): "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math. Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K. (with Usui, S.): "Logarithmic Hodge structures and classifying spaces (summary)"The arithmetic and geometry of algebraic cycles (Banff, Canada, 1998), CRM Proc. Lecture Notes. 24. 115-130 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K.: "Generalized explicit reciprocity laws"Algebraic number theory (Hapcheon/Saga, 1996), Adv. Stud. Contemp. Math. (Pusan). 1. 57-126 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "On the quadric hull of a canonical surface"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K. (with Ashikaga, T.): "Local and global properties of pencils of algebraic curves"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "1-2-3 theorem for curves on algebraic surfaces"J. reine angew. Math.. 533. 171-205 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K.: "Certain algebraic surfaces with non-reduced moduli space"Portugal. J. Math.. 57. 169-178 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Konno, K. (with Margarida Mendes Lopes): "On a question of Miles Reid"manuscripta math.. 100. 81-86 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E. (with Kachi, Y.): "Segre's reflexivity and an inductive characterization of hyperquadrics"Memoirs of A. M. S.. (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E. (with Zhao Yocai): "Smooth 4-folds which contains a P^1-bundle as an ample divisor"Manuscripta Math.. 101. 313-323 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E.: "Behavior of rational curves with the minimal degree in projective space bundle in any characteristic"J. Math. Kyoto Univ.. 40-4. 673-704 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E. (with Kachi, Y.): "Polarized varieties whose points are joined by rational curves of small degrees"Illinois J. Math.. 43-2. 350-390 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sato, E. (with Kachi, Y.): "Characterization of projective spaces and hyperquadrics"Proc. of Algebra Conference in memory of Kurosh, Moscow 1998, Walter de Gruyler, Berlin. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mori, S.: "On a hyperplane section theorem of Gurjar"Math. Ann.. 319. 533-537 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mori, S.: "Rational curves on algebraic varieties"Mathematics : Frontier and Perspectives (ed. by V. Arnold, M. Atiyah, P. Lax, and B. Mazur). 189-195 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mori, S. (with Fujino, O.): "A canonical bundle formula"J. Diff. Geom.. 56. 167-188 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sumihiro, H. (with Tagami, S.): "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math. J.. 31. 51-57 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Sumihiro, H.: "Determinantal varieties associated to rank two vector bundles on projective spaces and splitting theorems"Hiroshima Math. J.. 29. 371-434 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Infinitesimal logarithmic torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Higher normal functions and Griffiths groups"J. of Algebraic Geometry. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Motives, Algebraic Cycles and Hodge theory"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, CRM Proceedings and Lecture, A. M. S.. 24. 235-253 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "Motives and Filtrations on Chow groups, II"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, NATO Science Series, Kluwer Academic Publishers. 548. 321-346 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Saito, S.: "The Arithmetic and Geometry of Algebraic Cycles"The Arithmetic and Geometry of Algebraic Cycles, Proc. CRM Summer School, 1998, Banff, Canada, CRM Proceedings and Lecture, A. M. S.. 24. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "A compactification of the moduli scheme of abelian varieties"math AG/0107158 (e-print).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Plane cubic curves - from Hesse to Mumford"Sugaku, Iwanami Shoten. 53. 241-258 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Hilbert Schemes of abelian group orbits"J. Algebraic Geometry. 10. 757-779 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I. (with Terasoma, T.): "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proc. of Texel conference 1999, Progress in Math., Birkhauser. 195. 299-324 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I. (with Gomi, Y. and Shinoda, K.): "Hilbert schemes of G-orbits in dimension three"Kodaira's issue, Asian J. Math.. 4. 51-70 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I.: "Stability of degenerate abelian varieties"Invent. Math.. 136. 659-715 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I. (with Ito, Y.): "Hilbert schemes and simple singularities"New trends in algebraic geometry, Proc. European Math. Conference 1996, London Math. Soc., Lecture Note Series, Cambridge university press. 264. 151-233 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Nakamura, I. (with Alexeev, V.): "On Mumford's construction of degenerating abelian varieties"Tohoku Math. J.. 51. 399-420 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Counter-example to global Torelli problem for irreducible symplectic manifolds"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "A note on symplectic singularities"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International J. Math.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Deformation theory of Calabi-Yaus"Sugaku Exposition, A. M. S.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Stratified local moduli of Calabi-Yau threefolds"Topology. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Extension of 2-forms and symplectic varieties"J. Reine Angew. Math.. 539. 123-147 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Deformation theory of singular symplectic n-folds"Math. Ann.. 319. 597-623 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Namikawa, Y.: "Global smoothing of Calabi-Yau threefolds II"Compositio Math.. 125. 55-68 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mukai, S: "Moduli Theory I, II Perspective of Contemporary Mathematics #13, 14 (ed. Aomoto, K.) (in Japanese)"Iwatani Shoten. xiv + 175 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mukai, S: "Moduli Theory I, II Perspective of Contemporary Mathematics #13, 14 (ed. Aomoto, K.) (in Japanese)"Iwatani Shoten. xi + 280 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Ishida, M.: "Foundation of Algebraic Geometry (in Japanese)"Baifu-kan. 232 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Ishida, M.: "Introduction to Toric Varieties (Landscape of Mathematics 2) (in Japanese)"Asakura Shoten. 155 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Kato, K., Usui, S.: "Logarithmic Hodge structures and their moduli"(preprint).

    • Related Report
      2001 Annual Research Report
  • [Publications] Kato, K., Usui, S.: "Borel-Serre spaces and spaces of SL(2)-orbits"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Usui, S.: "Recovery of vanishing cycles by log geometry"Tohoku Math. J. 53-1. 1-36 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kato, K.(with Matsubara, T., Nakayama, C.: "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math.: Algebraic Geometry 2000, Azumino. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] 向井茂: "Verlinde公式の幾何学"数理解析研究所講究録「組合せ論的表現論をめぐる話題,2000年10月」. (採用予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Konno, K.: "On the quadric hull of a canonical surface"(preprint).

    • Related Report
      2001 Annual Research Report
  • [Publications] Konno, K.(with Ashikaga, T.): "Local and global properties of pencils of algebraic curves"(prepribt).

    • Related Report
      2001 Annual Research Report
  • [Publications] Konno, K.: "1-2-3 theorem for curves on algebraic surfaces"J. reine angew. Math.. 533. 171-205 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sato, E.(with Kachi, Y.): "Segre's reflexivity and an inductive characterization of hyperquadrics"Memoirs of A. M. S.. (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Mori, S.: "On a hyperplane section theorem of Gurjar"Math. Ann. 319. 533-537 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Sumihiro, H.(with Tagami, S.): "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math. J. 31. 51-57 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Saito, S.: "Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math.:Algebraic Geometry 2000, Azumino. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Saito, S.: "Higher normal functions and Griffiths groups"J. of Algebraic Geometry. 11・1. 161-201 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Nakamura, I.: "A compactification of the moduli scheme of abelian varieties"mathAG/0107158(e-print).

    • Related Report
      2001 Annual Research Report
  • [Publications] Nakamura, I.: "Plane cubic curves-from Hesse to Mumford"Sugaku, 岩波書店. 53. 241-258 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Nakamura, I.: "Hilbert schemes of abelian group orbits"J. Algebraic Geometry. 10. 757-779 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Nakamura, I(with Terasoma, T.): "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proc. of Texel conference 1999, Progress in Math., Birkhauser. 195. 299-324 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Counter-example to global Torelli problem for irreducible symplectic manifolds"(preprint).

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "A note on symplectic singularities"(preprint).

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International J. Math. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Deformation theory of Calabi-Yaus"Sugaku Exposition, A.M.S. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Stratified local moduli of Calabi-Yau threefolds"Topology. (to appear).

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Extension of 2-forms and symplectic varieties"J. Reine Angew. Math.. 539. 123-147 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Deformation theory of singular symplectic n-folds"Math. Ann. 319. 597-623 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Namikawa, Y.: "Global smootyhing of Calabi-Yau threefolds II"Compositio Math.. 125. 55-68 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Usui,S.: "Recovery of vanishing cycles by log geometry"Tohoku Math.J.. 53-1. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] Usui,S.: "Torelli type problems"Sugaku Expositions,Amer.Math.Soc.. 13. 17-38 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kato,K.and Usui,S.: "Borel-Serre spaces and spaces of SL (2) -orbits"Advanced Studies in Pure Math.. (under referee).

    • Related Report
      2000 Annual Research Report
  • [Publications] Kato,K.,Matsubara,T.and Nakayama,C.: "Log C^∞-functions and degenerations of Hodge structures"Advanced Studies in Pure Math.. (under referee).

    • Related Report
      2000 Annual Research Report
  • [Publications] 向井茂: "曲線と「曲面」をめぐって(数学の未解決問題17)"数理科学. 1月号. 56-64 (2000)

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      2000 Annual Research Report
  • [Publications] Ishida,M.: "Intersection complexes of fans and toric varieties"math.AG/0102085.

    • Related Report
      2000 Annual Research Report
  • [Publications] Konno,K.: "Certain algebraic surfaces with non-reduced moduli space"Portugal J.Math.. 57. 169-178 (2000)

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      2000 Annual Research Report
  • [Publications] Konno,K.: "1-2-3 theorem for curves on algebraic surfaces"J.reine angew.Math.. (in press).

    • Related Report
      2000 Annual Research Report
  • [Publications] Konno,K.: "Relations in canonical algebras on surfaces"

    • Related Report
      2000 Annual Research Report
  • [Publications] Sato,E.: "Behavior of rational curves with minimal degree in projective space bundle in any characteristic"J.Math.Kyoto Univ.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Sato,E.and Zhao,Y.: "Smoth 4-folds which contain a P′- bundle as an ample divisor"Manuscripta Math.. 101. 313-323 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Mori,S.: "On a hyperplane section theorem of Gurjar"Math.Annalen. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Kollar,J.,Miyaoka,Y,Mori,S.,and Takagi,H.: "Boundedness of canonical Q-Fano 3-folds"Proc.Japan Acad.,Ser.A Math.Sci.. 76. 73-77 (2000)

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      2000 Annual Research Report
  • [Publications] Fujino,O.and Mori,S.: "A canonical bundle formula"J.Diff.Geom.. (accepted).

    • Related Report
      2000 Annual Research Report
  • [Publications] Sumihiro,H.and Tagami,S.: "A splitting theorem for rank two vector bundles on projective spaces in positive characteristic"Hiroshima Math.J.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Saito,S.: "Infinitesimal logarithmic Torelli problem for degenerating hypersurfaces in P^n"Advanced Studies in Pure Math.. (under referee).

    • Related Report
      2000 Annual Research Report
  • [Publications] Nakamura,I.: "Hilbert schemes of abelian group orbits"J.Alg.Geom.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Gomi,Y.,Nakamura,I.and Shinoda,K.: "Hilbert schemes of G-orbits in dimension three"Asian J.Math.. 4. 1-20 (2000)

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      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "Calabi-Yaus and deformation theory"Sugaku Expositions, Amer.Math.Soc.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "Global smoothing of Calabi-Yau threefolds II"Compsitio Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "Deformation theory of singular symplectic n-folds"Math.Annalen. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "Extension of 2-forms and symplectic varieties"J.reine angew.Math.. (to appear).

    • Related Report
      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "A note on symplectic singularities"Math.AG/0101028.

    • Related Report
      2000 Annual Research Report
  • [Publications] Namikawa,Y.: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"Math.AG/0101019.

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      2000 Annual Research Report
  • [Publications] 向井茂: "モジュライ理論II,現在数学の展開"岩波書店. 291 (2000)

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      2000 Annual Research Report
  • [Publications] 石田正典: "トーリック多様体入門"朝倉書店(出版予定).

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      2000 Annual Research Report
  • [Publications] 石田正典: "代数幾何学の基礎"培風館. (2000)

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      2000 Annual Research Report
  • [Publications] Usui,S.: "Recovery of vanishing cycles by log geometry : Case of several variables"Communtative Algebra and Algebraic Geometry, and Computational Methods : ed. D.Eisenbud,Springer-Verlag. 133-143 (1999)

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      1999 Annual Research Report
  • [Publications] Kato,K. and Usui,S: "Logarithmic Hodge structures and their classifying spaces"Proc.NATO Advanced Study Institute/CRM Summer School 1998, Banff,Canada. (1999)

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      1999 Annual Research Report
  • [Publications] Kato,K. and Usui,S: "Logarithmic Hodge structures and their moduli (Main results)"to appear in Proc.of 'Hodge Theory and Algebraic Geometry 1999, Kagoshima Univ.. (to appear).

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      1999 Annual Research Report
  • [Publications] Kato,K. and Usui,S: "Logarithmic Hodge structures and their moduli (The fundamental diagram)"to appear in Proc.「退化・被覆・特異点の代数幾何とトポロジー」研究集会2000,東北学院大学. (to appear).

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      1999 Annual Research Report
  • [Publications] Konno,K.: "Clifford index and the slope of fibered surfaces"J.Alg.Geom.. 8. 207-220 (1999)

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      1999 Annual Research Report
  • [Publications] Konno,K. and Lopes,M.M.: "On a question of Miles Reid"manuscripta math.. 100. 81-86 (1999)

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      1999 Annual Research Report
  • [Publications] Kachi,Y. and Sato,E.: "Polarized varieties whose points are joined by rational curves of small degrees"Illinois J.Math.. 43-2. 350-390 (1999)

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      1999 Annual Research Report
  • [Publications] Sato,E. and Zhao,Y.: "Smooth 4-folds which contains a P'-bubdle as an ample divisor"Math.Z.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Mori,S.: "Rational curves on algebraic varieties"'Mathematics : Frontier and Perspectives' ed. V.Arnold,M.Atiyah,P.Lax and B.Mazur, A.M.S.2000. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Sumihiro,H.: "Determinantal varieties associated to rank two vector bundles on prejective spaces and splitting theorems"Hiroshima Math.J.. 29-2. 371-434 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Ito,Y.and Nakamura,I.: "Hilbert schemes and simple singularities"New trends in algebraic geometry;London Math.Soc.Lecture Note Series. 264. 151-233 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Alexeev,V.and Nakamura,I.: "On Mumford's construction of degenerating abelian varieties"Tohoku Math.J.. 51. 399-420 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Nakamura,I.: "Stability of degenerate abelian varieties"Invent,Math.. 136. 659-715 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Nakamura,I.: "Hilbert schemes of abelian group orbits"J.Alg.Geom.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Namikawa,Y.: "Global smoothing of Calabi-Yau three folds II"Comp.Math.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Namikawa,Y.: "Calabi-Yaus and Deformation theory"Sugaku exposition, A.M.S.. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] 向井 茂: "現代数学の展開:モジュライ理論II"岩波書店. (2000)

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      1999 Annual Research Report
  • [Publications] 石田正典: "トーリック多様体入門"朝倉書店(出版予定).

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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