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2007 Fiscal Year Final Research Report Summary

Research of Endomorphisms on projective algebraic varieties

Research Project

Project/Area Number 18540023
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNara Medical University (2007)
Gifu University (2006)

Principal Investigator

FUJIMOTO Yoshio  Nara Medical University, Medical department, Professor (90192731)

Project Period (FY) 2006 – 2007
Keywordsendomorphism / minimal model theory / algebraic geometr / complex manifold / elliptic fiber space
Research Abstract

The purpose of this research is to study the structure of smooth projective varieties X admitting a non-isomorphic surjective holomorphic map from X to itself which is called a nontrivial surjective endomorphism. Elliptic curves, abelian varieties, toric varieties etc. are typical examples of such varieties. And it is expected to have the very simple structure. In complex dynamical systems, a nontrivial surjective endomorphism on complex projective spaces and K3 surfaces has been mainly studied. Our viewpoint is to study the structure of the variety itself in view of the classification theory of algebraic varieties, not the endomorphism f. We have obtained a complete classification of smooth projective 3-folds with non-negative Kodaira dimension admitting a nontrivial surjective endomorphism. In 2002, the author has almost classified such varieties except one case and such exception has been solved in the joint work with Noboru Nakayama.

  • Research Products

    (6 results)

All 2007 2006

All Journal Article (2 results) (of which Peer Reviewed: 1 results) Presentation (4 results)

  • [Journal Article] Endomorphisms of smooth projective 3-folds with nonnegative Kodaira dimension,II2007

    • Author(s)
      Yoshio Fujimoto
    • Journal Title

      Journal of Mathematics of Kyoto University 47

      Pages: 79-114

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] Endomorphisms of smooth projective 3-folds with Nonnegative Kodaira dimension, II2007

    • Author(s)
      Yoshio, Fujimoto
    • Journal Title

      Journal of Mathematics of Kyoto University Vol. 47

      Pages: 79-114

    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Endomorphisms of smooth projective 3-folds with nonnegative Kodaira dimension,II2007

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      ベクトル束と高次元代数多様体
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-07-05
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Endomorphisms of smooth projective 3-folds with nonnegative Kodaira Dimension, II2007

    • Organizer
      Vector bundles and higher dimensional Algebraic geometry
    • Place of Presentation
      Kyoto University
    • Year and Date
      2007-07-05
    • Description
      「研究成果報告書概要(欧文)」より
  • [Presentation] Endomorphisms of smooth projective 3-folds with nonnegative Kodaira dimension,II2006

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      日本数学会秋季会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-21
    • Description
      「研究成果報告書概要(和文)」より
  • [Presentation] Endomorphisms of smooth projective 3-folds with nonnegative Kodaira Dimension, II2006

    • Organizer
      Nihon Sugaku kai
    • Place of Presentation
      Osaka City University
    • Year and Date
      2006-09-21
    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2010-02-04  

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