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study of endomorphisms of projective algebraic varieties

Research Project

Project/Area Number 20540048
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNara Medical University

Principal Investigator

FUJIMOTO Yoshio  Nara Medical University, 医学科, 教授 (90192731)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords代数学 / 幾何学 / 代数幾何学 / 複素多様体論 / 自己準同型写像 / 楕円ファイバー空間
Research Abstract

We have studied the structure of smooth projective 3-fold X with negative Kodaira dimension admitting non-isomorphic etale endomorphisms. The trouble is that there may exist KX-negative extremal rays which are not preserved by any power of f. However, by replacing f by a composite with a suitable automorphism of X, minimal model programs work in the category of etale edomorphisms in many cases. We have classified the candidate of such a variety X.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (10 results)

All 2010 2008 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (4 results) Remarks (1 results)

  • [Journal Article] Termination of extremal rays of fibration type for the iteration of Surjective endomorphisms2010

    • Author(s)
      Yoshio Fujimoto, Noboru Nakayama
    • Journal Title

      Compositio Math.(Appendix to D.-Q. Zhang's paper) 146

      Pages: 164-168

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Appendix. Termination of extremal rays of fibration type for the iteration of surjective endomorphisms2010

    • Author(s)
      Yoshio Fujimoto, Noboru Nakayama
    • Journal Title

      Compositio Math

      Volume: 146 Pages: 164-168

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Termination of extremal rays of fibration type for the iteration of surjective endomorphisms. (Appendix to D.-Q Zhang's paper)2010

    • Author(s)
      Yoshio Fujimoto, Noboru Nakayama
    • Journal Title

      Compositio Math Vol.146(1)

      Pages: 166-168

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Complex projective manifolds which admit non-isomorphic surjective Endomorphisms2008

    • Author(s)
      Yoshio Fujimoto, Noboru Nakayama
    • Journal Title

      RIMS Kokyuroku Bessatsu, B 9

      Pages: 51-79

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Complex projective manifolds which admit non-isomorphic surjective endomorphisms2008

    • Author(s)
      Fujimoto Yoshio, Nakayama Noboru
    • Journal Title

      RIMS Kokyuroku Bessatsu B9

      Pages: 51-79

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension.2010

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      研究集会:代数幾何学とその周辺
    • Place of Presentation
      高知大学理学部
    • Year and Date
      2010-12-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension2010

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      研究集会"代数幾何学とその周辺"
    • Place of Presentation
      高知大学理学部
    • Year and Date
      2010-12-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Smooth projective 3-folds with negative Kodaira dimension admitting non-isomorphic etale endomorphisms2008

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      シンポジューム:代数幾何学とその新しい展開
    • Place of Presentation
      京都大学理学部数学教室
    • Year and Date
      2008-11-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Smooth projective 3-folds with negative Kodaira dimension admitting non-isomorphic etale endomorphisms2008

    • Author(s)
      Fujimoto Yoshio
    • Organizer
      シンポジューム‘代数幾何学とその新しい展開'
    • Place of Presentation
      京都大学理学部数学教室
    • Year and Date
      2008-11-22
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等 なし

    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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