study of endomorphisms of projective algebraic varieties

射影代数簇的自同态研究

• 批准号: 20540048
• 负责人: FUJIMOTO Yoshio
• 金额: $ 1.75万
• 依托单位: Nara Medical University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540048/
• 关键词: 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

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.

本文研究了具有负科代拉维数且允许非同构的根自同态的光滑投射3重X的结构。问题是可能存在KX-负极值射线，它们不被f的任何幂保持。然而，通过将f替换为具有X的适当自同构的复合，极小模型程序在许多情况下工作在etale自同态范畴中。我们已经将这样一个簇X的候选者分类。

项目成果

Termination of extremal rays of fibration type for the iteration of Surjective endomorphisms

满射自同态迭代的纤维化型极值射线的终止

• 发表时间: 2010
• 期刊: Compositio Math.(Appendix to D.-Q. Zhang's paper) 146
• 作者: Yoshio Fujimoto;Noboru Nakayama
• 通讯作者: Noboru Nakayama

Termination of extremal rays of fibration type for the iteration of surjective endomorphisms. (Appendix to D.-Q Zhang's paper)

满射自同态迭代的纤维化型极值射线的终止。

• 发表时间: 2010
• 期刊: Compositio Math Vol.146(1)
• 作者: Yoshio Fujimoto;Noboru Nakayama
• 通讯作者: Noboru Nakayama

Complex projective manifolds which admit non-isomorphic surjective Endomorphisms

允许非同构满射内同态的复射影流形

• 发表时间: 2008
• 期刊: RIMS Kokyuroku Bessatsu, B 9
• 作者: Yoshio Fujimoto;Noboru Nakayama
• 通讯作者: Noboru Nakayama

Etale endomorphisms of smooth projective 3-folds with negative Kodaira dimension.

具有负 Kodaira 维数的平滑投影 3 重的 Etale 自同态。

• 发表时间: 2010
• 作者: Fujimoto Yoshio;Nakayama Noboru;Yoshio Fujimoto
• 通讯作者: Yoshio Fujimoto

Smooth projective 3-folds with negative Kodaira dimension admitting non-isomorphic etale endomorphisms

具有负 Kodaira 维数的平滑投影 3 重，允许非同构 etale 自同态

• 发表时间: 2008
• 作者: Fujimoto Yoshio;Nakayama Noboru;Yoshio Fujimoto;Yoshio Fujimoto;Yoshio Fujimoto
• 通讯作者: Yoshio Fujimoto