study of endomorphisms of projective algebraic varieties

• Project/Area Number: 20540048
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Nara 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: ¥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.

Research Products

• [Journal Article] Termination of extremal rays of fibration type for the iteration of Surjective endomorphisms (2010)
  • Author(s): Yoshio Fujimoto, Noboru Nakayama
  • Journal Title: Compositio Math.(Appendix to D.-Q. Zhang's paper) 146 Pages: 164-168
  • Peer Reviewed
• [Journal Article] Appendix. Termination of extremal rays of fibration type for the iteration of surjective endomorphisms (2010)
  • Author(s): Yoshio Fujimoto, Noboru Nakayama
  • Journal Title: Compositio Math Volume: 146 Pages: 164-168
  • 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
  • Peer Reviewed
• [Journal Article] Complex projective manifolds which admit non-isomorphic surjective Endomorphisms (2008)
  • Author(s): Yoshio Fujimoto, Noboru Nakayama
  • Journal Title: RIMS Kokyuroku Bessatsu, B 9 Pages: 51-79
  • Peer Reviewed
• [Journal Article] Complex projective manifolds which admit non-isomorphic surjective endomorphisms (2008)
  • Author(s): Fujimoto Yoshio, Nakayama Noboru
  • Journal Title: RIMS Kokyuroku Bessatsu B9 Pages: 51-79
  • 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
• [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
• [Presentation] Smooth projective 3-folds with negative Kodaira dimension admitting non-isomorphic etale endomorphisms (2008)
  • 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
• [Presentation] Smooth projective 3-folds with negative Kodaira dimension admitting non-isomorphic etale endomorphisms (2008)
  • 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
• [Remarks] ホームページ等 なし