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2001 Fiscal Year Final Research Report Summary

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
KeywordsLogarithmic Hodge Theory / Compactifications of Moduli / Invariant Functions / Torelli Problem / Algebraic Varieties / Canonical Rings / Vector Bundles / Symplectic Varieties
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.

  • Research Products

    (105 results)

All Other

All Publications (105 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [Publications] Nakamura, I.: "Plane cubic curves-from Hesse to Mumford"Sugaku,岩波書店. 53. 241-258 (2001)

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

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

    • Description
      「研究成果報告書概要(和文)」より
  • [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
  • [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
  • [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
  • [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
  • [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(和文)」より
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [Publications] Namikawa, Y.: "A note on symplectic singularities"(Preprint).

    • Description
      「研究成果報告書概要(欧文)」より
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 2003-09-17  

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