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Quasiprojectivity of moduli spaces of algebraic varieties

Research Project

Project/Area Number 12640064
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Institute of Technology

Principal Investigator

TSUJI Hajime  Tokyo Institute of Technology, Department of Mathematics, Associate Professor, 大学院・理工学研究科, 助教授 (30172000)

Co-Investigator(Kenkyū-buntansha) FUJITA Takao  Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (40092324)
ISHII Shihoko  Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (60202933)
FUTAKI Akito  Tokyo Institute of Technology, Department of Mathematics, Professor, 大学院・理工学研究科, 教授 (90143247)
HATTORI Toshiaki  Tokyo Institute of Technology, Department of Mathematics, Associate Professor, 大学院・理工学研究科, 助手 (30251599)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
Keywordsmoduli space / plurigera / vareiteis of general type / multiplier ideal sheaves / 多重標準系 / 劣随伴定理 / Flip / 概代数性
Research Abstract

We proved that the quasiprojectivity of moduli spaces of nonsingular projective varieties in general.
It will appear as a joint paper with G.Schumacher (Annals of Mathematics 159).
I also proved that the deformation invariance of plurigenera for projective deformations of projective Manifolds. This is a very fundamental result in algebraic geometry.
Also I proved that there exsists a positive constant $nu_{n}$ such that for every $m geqq nu_{n}$ and every projective $n$-fold of general type $X$, $mK_{X}$ gives a birational embedding of $X$.
This is also very fundamental result in algebraic geometry.

Report

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

    (13 results)

All 2004 2002 2001 Other

All Journal Article (5 results) Book (1 results) Publications (7 results)

  • [Journal Article] Quasiprojectivity of moduli spaces of polarized algebraic varieties2004

    • Author(s)
      H.Tsuji (with G.Schumacher)
    • Journal Title

      Annals of Mathematics 159

      Pages: 599-641

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Journal Article] Quasiprojectivity of moduli spaces of algebraic varieties2004

    • Journal Title

      Annals of Math. 159(to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Journal Article] Deformation invarianve of plurigenera2002

    • Author(s)
      H.Tsuji
    • Journal Title

      Nagoya Math. J. 166

      Pages: 117-134

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Journal Article] Deformation invariance of plurigenera2002

    • Journal Title

      Nagoya Math J. 166

      Pages: 117-134

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Journal Article] Subadjunction theorem for pluricanomical divisors

    • Author(s)
      H.Tsuji
    • Journal Title

      ASPM Proc. of Oka Centennial Symposium

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Book] Singular hermitian metrics in algebraic geometry2001

    • Author(s)
      H.Tsuji
    • Total Pages
      159
    • Publisher
      名古屋大学多元数理
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] H.Tsuji: "Deformation Invariance of Plurigenra"Nagoya Math.J.. 166. 117-134 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] G.Schumacher, H.Tsuji: "Quasiprojectivity of Moduli Spaces of Polarized Varieties"Annals of Mathematics. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] H.Tsuji: "Subadjunction Theorem"Proceedings of Oka 100. (to appear).

    • Related Report
      2002 Annual Research Report
  • [Publications] H.TSUJI: "Deformation invariance of plurigenera"Nagoya Math. J.. (掲載予定). (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] 辻 元: "Singular hermitiun metrics in Algebraic Geometry"名古屋大学. 153 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] H.Tsuji: "Deformation Invariance of Plural genera"Proc. of Hoyoma Symporlum 2000. (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] H.Tsuji: "Singula Hermitian metrian in Algebraic Geometry"名古屋大学多元数理学科. (2001)

    • Related Report
      2000 Annual Research Report

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

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