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Research on duality theorems of modules on fans

Research Project

Project/Area Number 12640006
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ISHIDA Masanori  Tohoku University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30124548)

Co-Investigator(Kenkyū-buntansha) KAJIWARA Takeshi  Tohoku University, Graduate School of Science, Research Assistant, 大学院・理学研究科, 助手 (00250663)
ITO Hiroyuki  Hiroshima University, Graduate School of engineering, Associate Professor, 大学院・工学研究科, 助教授 (60232469)
HARA Nobuo  Tohoku University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90298167)
Project Period (FY) 2000 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsalgebraic variety / toric variety / abelian variety / elliptic curve / blowup / Rees alebra / fan / 可換環 / 楕円曲面 / 強レフシェッツ定理 / K3曲面 / 双対化定理 / 交叉コホモロジー群 / 端末特異点
Research Abstract

Ishida studied on not necessarily rational fan as a generalization of the theory of toric varieties. He constructed the theory of Zariski-Riemann spaces of fans.
Hara defined the tight closure of ideals associated with a fixed ideals as a generalization of the theory of tight closures of ideals.
Ito studied on the Mordell-Weil lattices of elliptic curves from the view point of singularity theory and deformation theory.
Kajiwara studied on the Deligne conjecture on the l-adic etale cohomology of nonsingular algebraic varieties defined over a valuation ring.

Report

(5 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • 2000 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] 石田 正典: "実平面で作るトーリック多様体"数学セミナー. 3月号. 19-23 (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "Geometric interpretation of tight closure and test ideals"Trans.AMS. 353. 1885-1906 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "Kawachi's invariant for fat points"J.Pure Appl.Algebra. 165. 201-211 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "A characteristic p analog of multiplier ideals and applications"Comm.Algebra. printing. (2004)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Ito: "On extremal elliptic surfaces in characteristic 2 and 3"Hiroshima Mathematical Journal. 32. 179-188 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 梶原 健: "Abelian surfaces in toric 4-folds"研究集会「凸多面体を巡る組合せ論の代数的諸相」報告集. 1175. 123-131 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 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
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masanori Ishida: "Toric varieties made of real planes"Sugaku Seminar, March. 19-23 (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "Geometric interpretation of tight closure and test ideals"Trans.AMS. 353. 1885-1906 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "Kawachi's invariant for fat points"J.Pure Appl.Alebra. 165. 201-211 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Nobuo Hara: "A characterstic p analog of multiplier ideals and applications"Comm.Algebra. (printing). (2004)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Hiroyuki Ito: "On extremal elliptic surfaces in characteristics 2 and 3"Hiroshima Mathematical Journal. 32. 179-188 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takeshi Kajiwara: "Abelian surfaces in toric 4-folds"Proceedings of symposium "Algebraic aspects of combinatorics on convex polytopes". 1175. 123-131 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Masanori Ishida: "Basics of algebraic geometry"Baifukan. 232 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] 石田正典: "実平面で作るトーリック多様体"数学セミナー. 3月号. 19-23 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 原伸生, 渡辺敬一: "F-regular and F-pure rings vs log terminal and log canonical singularities"Journal of Algebraic Geometry. 11. 363-392 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 伊藤浩行: "On extremal elliptic surfaces in characteristic 2 and 3"Hiroshima Mathematical Journal. 32. 179-188 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 石田 正典: "扇の代数幾何における永田のコンパクト化と交叉複体"2001年度代数幾何学城崎シンポジウム報告集. (発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 原 伸生: "Kawachi's invariant for fat points"J.Pure Appl. Algebra. 165. 201-211 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] 伊藤 浩行: "On extremal elliplic surfaces in characteristic 2 and 3"Hiroshima Math.J.. (発表予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 原伸生: "Geometric interpretation of tight closure and test ideals"Trans.AMS. 353. 1885-1906 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] 石田正典: "代数幾何学の基礎"培風館. 232 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] 石田正典: "トーリック多様体入門"朝倉書店. 155 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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