• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2013 Fiscal Year Final Research Report

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

Research Project

  • PDF
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
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
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.

  • Research Products

    (5 results)

All 2014 2013 2011

All Journal Article (1 results) Presentation (4 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

  • [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
  • [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
  • [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
  • [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

URL: 

Published: 2015-07-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi