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A study of compact complex manifolds admitting non-isomorphic surjective endomorphisms

Research Project

Project/Area Number 23540055
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionNara Medical University

Principal Investigator

FUJIMOTO Yoshio  奈良県立医科大学, 医学部, 教授 (90192731)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords自己正則写像 / 端射線 / コニック束 / 半安定ベクトル束 / 楕円繊維曲面 / 楕円ファイバー空間 / 極小モデル計画 / 極小モデルプログラム / del Pezzo束 / 有理連結多様体 / endomorphism / extremal ray / conic bundle / DESP / Atiyah / Del-Pezzo bundle
Research Abstract

We have studied structures of smooth projective 3-folds X with negative Kodaira dimension admitting non-isomorphic \'{e}tale endomorphisms. We can show that a suitable finite \'{e}tale covering X' of X is classified into 6 types. There exists some X where X' cannot be decomposed as a product of a uniruled surface and an elliptic curve. The contraction morphism associated to R is the inverse of a blow-up of another smooth 3-fold along an elliptic curve. The trouble is that R cannot necessarily be stabilized by a suitable power of f. Hence the minimal model program(MMP) cannot work so as to be compatible with endomorphisms. As a substitute, we consider the tower of non-isomorphic finite \'{e}tale covering of 3-folds (called ESP), on which MMP works well. Such a 3-fold X can be obtained as a succession of blow-ups along an elliptic curve from a characteristic ESP (called DESP). We can also give a simple criterion for certan conic bundles to have non-isomorphic \'{e}tale endomorphisms.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (10 results)

All 2014 2013 2011 Other

All Journal Article (2 results) Presentation (8 results)

  • [Journal Article] Étale endomorphisms of smooth projective 3-folds with negative Kodaira dimension2011

    • Author(s)
      Yoshio Fujimoto
    • Journal Title

      射影多様体の幾何とその周辺2011高知大学シンポジューム報告集

      Pages: 45-60

    • Related Report
      2013 Final Research Report
  • [Journal Article] Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension2011

    • Author(s)
      藤本圭男
    • Journal Title

      射影多様体の幾何とその周辺2011報告集

      Volume: 11 Pages: 45-60

    • Related Report
      2011 Research-status Report
  • [Presentation] 射影代数多様体の上の自己準同型写像2014

    • Author(s)
      Yoshio Fujioto
    • Organizer
      代数学放談会
    • Place of Presentation
      岡山大学
    • Year and Date
      2014-01-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Étale endomorphisms of smooth projective 3-folds2013

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      アフィン代数幾何学研究会
    • Place of Presentation
      関西学院大学
    • Year and Date
      2013-09-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Étale endomorphisms of smooth projective 3-folds with negative Kodaira dimension2011

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      複素代数幾何セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-12-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Étale endomorphisms of smooth projective 3-folds with negative Kodaira dimension dimension2011

    • Author(s)
      Yoshio Fujimoto
    • Organizer
      研究集会 : 射影多様体の幾何とその周辺
    • Place of Presentation
      高知大学理学部
    • Year and Date
      2011-11-03
    • Related Report
      2013 Final Research Report
  • [Presentation] \'{E}tale endomorphisms of smooth projective 3-folds

    • Author(s)
      藤本圭男
    • Organizer
      第12回 affine 代数幾何学研究集会
    • Place of Presentation
      関西学院大学大阪梅田キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] 射影代数多様体の上の自己準同型写像

    • Author(s)
      藤本圭男
    • Organizer
      岡山大学・代数学放談会
    • Place of Presentation
      岡山大学理学部数学教室
    • Related Report
      2013 Annual Research Report
  • [Presentation] Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension

    • Author(s)
      藤本圭男
    • Organizer
      研究集会・射影多様体の幾何とその周辺(招待講演)
    • Place of Presentation
      高知大学理学部数学教室
    • Related Report
      2011 Research-status Report
  • [Presentation] Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension

    • Author(s)
      藤本圭男
    • Organizer
      大阪大学・複素代数幾何セミナー
    • Place of Presentation
      大阪大学理学部数学教室
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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