Analysis of structures on affine algebraic varieties from the viewpoint of log minimal model theory

从对数极小模型理论角度分析仿射代数簇的结构

• 批准号: 20740004
• 负责人: KISHIMOTO Takashi
• 金额: $ 2.75万
• 依托单位: Saitama University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 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-20740004/
• 关键词: アフィン代数幾何学; 双有理幾何学; 加法群スキーム作用; 加法群作用; 局所冪ゼロ導分; ログ極小モデル理論; アフィン代数多様体; 群作用付き多様体; サルキソフ・プログラム

In the present project of research, I devoted mainly myself to the analysis of structures on affine algebraic varieties from the various points of view. More precisely, in the first viewpoint, I succeeded into the translation of the existence of actions of a 1-dimensional additive group on affine cones over polarized projective varieties into the existence of certain kinds of open subset contained in the polarized varieties. In the second, I could reduce the homogeneous action of a 1-dimensional additive group on the affine 3-space to linear pencil of rational curves with special properties on weighted projective planes to be able to produce plenty of complicated automorphisms.

在目前的研究项目中，我主要致力于从各种角度分析仿射代数簇的结构。更确切地说，在第一个观点，我成功地翻译的存在行动的1维添加剂组仿射锥极化投影品种到存在的某些种类的开子集中所载的极化品种。在第二种方法中，我可以将仿射3-空间上的1维加法群的齐次作用归结为在加权射影平面上具有特殊性质的有理曲线的线性束，以便能够产生大量复杂的自同构。

项目成果

G_a and C_a^2-actions on the complements of hypersurfaces in P^n

G_a 和 C_a^2 - 对 P^n 中超曲面的补集的作用

• 发表时间: 2011
• 作者: Alessio Corti;James McKernan and Hiromichi Takagi;Shinobu Hosono and Hiromichi Takagi;Takashi Kishimoto
• 通讯作者: Takashi Kishimoto

Homogeneous locally nilpotent derivations of C[x, y, z] and pencils of rational plane curves

C[x, y, z] 的齐次局部幂零导数和有理平面曲线的铅笔

• 发表时间: 2011
• 期刊: RIMS Kokyuroku Bessatsu B24
• 作者: 須田庄;田中太初;田中太初;田中太初;Hajime Tanaka;田中太初;Hajime Tanaka;Takashi Kishimoto
• 通讯作者: Takashi Kishimoto

Homogeneous locally nilpotent derivations of C[x,y,z] and pencils of rational plane curves

C[x,y,z] 的齐次局部幂零导数和有理平面曲线的铅笔

• 发表时间: 2011
• 期刊: RIMS Kokyuroku Bessatsu
• 作者: 須田庄;田中太初;田中太初;田中太初;Hajime Tanaka;田中太初;Hajime Tanaka;Takashi Kishimoto;Takashi Kishimoto
• 通讯作者: Takashi Kishimoto

An application of log minimal model program for affine algebraic threefolds

仿射代数三重对数最小模型程序的应用

• 发表时间: 2008
• 作者: 伊吹山知義;若槻聡;高木寛通;岡耕平;Takashi KISHIMOTO
• 通讯作者: Takashi KISHIMOTO

An application of log minimal model program to affine algebraic threefolds

对数最小模型程序在仿射代数三重中的应用

• 发表时间: 2010
• 作者: H.Takagi;F.Zucconi;Takashi Kishimoto
• 通讯作者: Takashi Kishimoto