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Problems on Manifolds

Research Project

Project/Area Number 62460002
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionTOHOKU UNIVERSITY

Principal Investigator

ODA Tadao Professor  Faculty of Science,Tohoku University, 理学部, 教授 (60022555)

Co-Investigator(Kenkyū-buntansha) BANDO Shigetoshi Assista  Faculty of Science,Tohoku University, 理学部, 助教授 (40165064)
ISHIDA Masa-Nori Assista  Faculty of Science,Tohoku University, 理学部, 助教授 (30124548)
森田 康夫  東北大学, 理学部, 教授 (20011653)
HOTTA Ryoshi Professor  Faculty of Science,Tohoku University, 理学部, 教授 (70028190)
SATAKE Ichiro Professor  Faculty of Science,Tohoku University, 理学部, 教授 (00133934)
MORITA Yasuo Professor  Faculty of Science,Tohoku University
Project Period (FY) 1987 – 1988
Project Status Completed (Fiscal Year 1988)
Budget Amount *help
¥4,600,000 (Direct Cost: ¥4,600,000)
Fiscal Year 1988: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1987: ¥2,600,000 (Direct Cost: ¥2,600,000)
KeywordsAlgebraic singularity / Complex analytic singularity / Toric variety / Zeta function / Affine Lie algebra / Conformal field theory / アインシュタイン・ケーラー計量 / ゼータ函数 / L函数 / ケーラー計量 / アヤィン・リー環 / トーリック因子 / 非ケーラー多様体 / 共形的場の理論 / アフィンワイル群 / ヘッケ環
Research Abstract

1. We carried out investigations of algebraic and complex analytic singularities: (1) Analysis of infinitely very near singular points in arbitrary characteristics. (2) General theoretical formulation of the notion of toric divisors. (3) Construction of many new non-Kaehler manifolds.
2. In connection with automorphic functions, we studied zeta functions, L-functions from the point of view of their functional equations, residues and special values. We could find various important connections with the geometric properties of manifolds.
3. We carried out the following research on algebraic varieties and complex manifolds: (1) Birational geometry of toric varieties. (2) Unequal characteristic non-singular lifting of varieties with normal crossings. (3) Ricci-flat Kaehler metrics on affine algebraic manifolds. (4) Torelli problem for complete intersection varieties. (5) Construction and numerical invariants of regular algebraic surfaces of general type.
4. We carried out Lie-group-theoretic study of bounded domains as well as algebro-analytic study of Lie groups, algebraic groups, affine Lie algebras and their representations.
5. We could formulate two-dimensional conformal field theory in the framework of arithmetic algebraic geometry.
6. We exchanged research information with mathematicians inside and outside japan.

Report

(3 results)
  • 1988 Annual Research Report   Final Research Report Summary
  • 1987 Annual Research Report
  • Research Products

    (74 results)

All Other

All Publications (74 results)

  • [Publications] ODA,Tadao: Advanced Studies in Pure Math.8. 363-404 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA,Tadao: Advanced Studies in Pure Math.10. 591-648 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA,Tadao: Proc.of Seminar in Algebraic Geometry,Singapore. 89-94 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SATAKE,Ichiro: Proc.of Ramanujan Intern.Colloq.,Tata Inst.(1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SATAKE,Ichiro;OGATA,Shoetsu: Advanced Studies in Pure Math.15. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] HOTTA,Ryoshi: 京都大学数理解析研究所講究録. 642. 40-66 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] MORITA,Yasuo: Algebraic Analysis. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] MORITA,Yasuo: Advanced Studies in Pure Math.17. (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ISHIDA,Masanori: Algebraic Geometry and Commutative Algebra. 141-154 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ISHIDA,Masanori: Tohoku Math.J.40. 367-396 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA,Tadao: "Convex Bodies and Algebraic Geometry" Springer-Verlag, 220 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA,Tadao: "Introduction to Algebraic Singularities" The Institute of Mathematical Sciences,Madras, (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] HOTTA,Ryoshi: "Introduction to D-modules" The Institute of Mathematical Sciences,Madras,

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: "Infinitely very near singular points." Advanced Studies in Pure Math.8. 363-404 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: "K. Saito's period map for holomorphic functions with isolated critical points." Advanced Studies in Pure Math.10. 591-648 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: "Convex bodies and algebraic geometry ---toric varieties and applications--- I" Proc. Slgebraic Geometry Seminar, Singapore. 89-94 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: "Birational geometry of compact toric varieties." In preparation.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SATAKE, Ichiro: "On zeta functions associated with self-dual homogeneous cones." Proc. Ramanujan Intern. Collog., Tata Inst.(1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SATAKE, Ichiro; OGATA, Shoetsu: "Zeta functions associated to cones and their special values." Advanced Studies in Pure Math.15. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] HOTTA, Ryoshi: "Character D-modules" Proc. Res. Inst. Math. Sc., Kyoto Univ.642. 40-66 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] MORITA, Yasuo: "A note on the Hilbert irreducibility theorem---the irreducibility theorem and the strong approximation theorem."

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] MORITA, Yasuo: "A p-adic theory of hyperfunctions, II" Algebraic Analysis. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] MORITA, Yasuo: "A lower bound of L_P(1,X) for a Dirichlet character X." Advanced Studies in Pure Math.17. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ISHIDA, Masa-Nori: "Local cohomology groups of an affine semigroup ring" Algebraic Geometry and Commutative Algebra. 141-154 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ISHIDA, Masa-Nori: "An elliptic surface covered by Mumford's fake projective plane" Tohoku Math. J.40. 367-396 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ISHIDA, Masa-Nori: "T-complexes and Ogata's zeta zero values" Advanced Studies in Pure Math.15. (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] BANDO, Shigetoshi: "The K-energy map, almost Einstein-Kaehler metrics and an inequality of Miyaoka-Yau type" Tohoku Math. J.39. 231-235 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] BANDO, Shigetoshi and KOBAYASHI, Ryoichi: "Ricci-flat Kaehler metrics on affine algebraic manifolds." Lecture Notes in Math. (Springer-Verlag). 1339. 20-31 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] BANDO, Shigetoshi and KOBAYASHI, Ryoichi: "Ricci-flat Kaehler metrics on affine algebraic manifolds, II" Inventiones Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: Convex Bodies and Algebraic Geometry. Springer-Verlag, 220 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] ODA, Tadao: Introduction to Algebraic Singularities.The Institute of Mathematical Sciences, Madras,

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] HOTTA, Ryoshi: Introduction to D-modules.The Institute of Mathematical Sciences, Madras, 196 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1988 Final Research Report Summary
  • [Publications] SATAKE,Ichiro: Proc.of Ramannjan:Collog.:Tate Inst.Bombay. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] SATAKE,Ichiro.;OGATA,Shoetu: Advanced Studies in Pure Math.15. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] HOTTA,Ryoshi: 京都大学数理解析研究所講究録. 642. 40-66 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] MORITA,Yasuo: Advanced Studies in Pure Marh.17. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] MORITA,Yasuo: Algebrain Analysis,Academic Press. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] SHIMIZU,Satoru: Tohoku Marh,J.40. 119-152 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] SHIMIZU,Satoru: Japanese J.Marh,. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] OGATA,Shoetsu: Duke Marh,T.

    • Related Report
      1988 Annual Research Report
  • [Publications] OGATA,Shoetsu: 投稿予定.

    • Related Report
      1988 Annual Research Report
  • [Publications] KATSURA,Toshiyuki;SHIMI U,Yuji;UENO,KENJI: Comm.Marh.Phys.

    • Related Report
      1988 Annual Research Report
  • [Publications] ISHIDA,Masanori: Advanced Studies in Pure Math. 15. (1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] ISIDA,Masanori: Tohoku Math.J. 40. 367-396 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] ISIDA,Masanori: Algebraci Geometry and Commutative Algebra Kinokuniya and Academic Press. 141-154 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] BAND,Sigetoshi;KOBAYASHI,Ryoichi: Lecture Notes in Math.,Springer-Verlag. 1339. 20-31 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] BAND,Sigetoshi;KOBAYASHI,Ryoichi: Inventiones Math.

    • Related Report
      1988 Annual Research Report
  • [Publications] KONNO,Kazuhiro: Duke Mah,T.(1989)

    • Related Report
      1988 Annual Research Report
  • [Publications] KONNO,Kazuhiro: J.Math,Sor, Japan. 40. 687-703 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] WATANABE,Takao: Tohoku Marh,J.40. 491-534 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] HASEGAWA,Koji: Publ.Res.Inst.Marh.Sei.,Kyoto Univ.

    • Related Report
      1988 Annual Research Report
  • [Publications] Ono,Kaoru: Pror,Amer.Marh.Soi. 102. 1071-1076 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Ono,Kaoru: Marh.Ann.281. 163-168 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Ono,Kaoru: J.Fac.Sai.Univ.Tokyo. 35. 381-392 (1988)

    • Related Report
      1988 Annual Research Report
  • [Publications] Ono,Kaoru: J.Fac.Sa.univ.Tokyo.

    • Related Report
      1988 Annual Research Report
  • [Publications] ODA,Tadao: Advanced Slndies in Pwu Mathemstice. 8. 363-404 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] ODA,Tadao: Adranced Stndis in Pure Majhimatics. 10. 591-648 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] ODA,Tadao: Pror of Seminar in Alydraic Geometry,Singapou. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] SATAKE,Ichiro;OGATA,Shoetsu: Advanced Studis in Pure Math. 15.

    • Related Report
      1987 Annual Research Report
  • [Publications] ISHIDA,Masanori: Advanced Studris in Pwre Math. 15.

    • Related Report
      1987 Annual Research Report
  • [Publications] ISHIDA,Masanori: Tohoku Math,J. 40. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] ISHIDA,Masanori: Algcbraci Germetcy and Commutaticy Algcbra in baror of Masayshi Nagata. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] BANDO,Shigetoshi: Tohoku Mslh,J. 39. 231-235 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] BANDO,Shigotoshi;KOBAYASHI,Ryoichi: Lecfvre Nodes in math,Springer-Velag.

    • Related Report
      1987 Annual Research Report
  • [Publications] TANISAKI,Toshiyuki: Publ,Res,Inst,Math,Sc,Kyoto Univ. 23. (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] TANISAKI,Toshiyuki: Advanced Studies in Pwe Math. 14. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] SHIMIZU,Satoru: Tohoku Math,J. 40. 119-152 (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] KOBAYASHI,Ryoichi;NARUKI,Isao: Advanced Studies in fure math. 15. (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] OGATA,Shoetsu: Tohoku Msth,J. 39. 237-248 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] KONNO,Kazuhiro: Dnki math,J.

    • Related Report
      1987 Annual Research Report
  • [Publications] ODA,Tadao: "Convix Bodies and Algebraui Geometoy" Springer-Verlag, 220 (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] ODA,Tadao: "Introduction to Algebrair Singulariteies" The Institvte of Mathematical Sceinces,Madras, (1988)

    • Related Report
      1987 Annual Research Report
  • [Publications] HOTTA,Ryoshi: "Introduction to D-modules" Institvte of Msjbewatical Sciences,Madras, (1987)

    • Related Report
      1987 Annual Research Report
  • [Publications] NAMBA,Makoto: "Branched Coverings and Algcbaic Functions" Longman Research Notes in Math,161, (1987)

    • Related Report
      1987 Annual Research Report

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Published: 1987-04-01   Modified: 2016-04-21  

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