Study of moduli of indecomposable modules and degeneration of modules

不可分解模的模和模的退化研究

• 批准号: 15340010
• 负责人: YOSHINO Yuji
• 金额: $ 6.85万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15340010/
• 关键词: commutative rings; Cohen-Macaulay modules; deformation and degeneration; 可換環; 直既約加群; 退化; Gorenstein次元; 加群; 導来圏; G次元; Cohen-Macaulay

As a joint work with Osamu Iyama (Nagoya Univ.), we have defined the mutation as an action of braid group on the set of indecomposable objects in a general triangulated category. We have developed a general theory of mutation and have applied it to the classification problem of rigid Cohen-Macaulay modules. In particular, we succeeded to describe the perfect classification of rigid Cohen-Macaulay modules over a Veronese subring of dimension 3 and of degree 3. Through this consideration of the mutation, we are able to obtain further examples as well where we can classify the rigid Cohen-Macaulay modules. Actually the study was done by considering the maximal orthogonal subcategories in the stable category of Cohen-Macaulay modules. An investigation of the similar problem in a derived category is now in progress.We also made a study on the deformation and the degeneration of modules. And we succeeded to construct a noncommutative parameter space of the universal deformations of a module. By this, we are now able to understand well the classical obstruction theory of modules. This noncommutative deformation theory is also in progress.

在与名古屋大学的Osamu Iyama的合作中，我们将突变定义为辫群对一般三角分类中不可分解对象集合的作用。我们发展了一种突变的一般理论，并将其应用于刚性Cohen-Macaulay模的分类问题。特别地，我们成功地描述了3维3次的Veronese子带上刚体Cohen-Macaulay模的完美分类。通过这种对突变的考虑，我们能够获得进一步的例子，我们也可以对刚性Cohen-Macaulay模块进行分类。实际上，研究是通过考虑Cohen-Macaulay模稳定范畴中的极大正交子范畴来完成的。目前正在对派生类中的类似问题进行调查。我们还对模组的变形和退化进行了研究。成功地构造了一个模的泛变形的非交换参数空间。由此，我们可以很好地理解经典模阻理论。这种非交换变形理论也在研究中。

项目成果

Cesar A.Escobar, Rafael H.Villarreal, Yuji Yoshino: "Torsion freeness and normality of associated graded rings and Rees algebras of monomial ideals"Lisbon Conference on Commutative Algebra, Marcel Dekker's Lecture Notes in Pure and Applied Mathematics Ser

Cesar A.Escobar、Rafael H.Villarreal、Yuji Yoshino：“关联分级环和单项式理想的里斯代数的扭转自由度和正态性”里斯本交换代数会议，Marcel Dekker 的纯粹与应用数学系列讲座笔记

Torsion freeness and normality of associated graded rings and Rees algebras of monomial ideals

相关分级环的扭转自由度和正态性以及单项式理想的里斯代数

• 发表时间: 2006
• 期刊: Lecture Notes in Pure and Applied Mathematics 244
• 作者: Cesar A.Escobar;Rafael H.Villarreal;Yuji Yoshino
• 通讯作者: Yuji Yoshino

Yuji Yoshino: "Degeneration and G-dimension of modules"Lisbon Conference on Commutative Algebra, Marcel Dekker's Lecture Notes in Pure and Applied Mathematics Series. (To appear). (2004)

Yuji Yoshino：“模的退化和 G 维”里斯本交换代数会议，Marcel Dekker 的纯粹与应用数学系列讲座笔记。

On a group graded version of BGG

BGG 的团体评分版本

• 发表时间: 2007
• 期刊: Communications in Algebra 35
• 作者: E. L. Green;R. Martinez-Villa and Y. Yoshino
• 通讯作者: R. Martinez-Villa and Y. Yoshino

Characterizing Cohen-Macaulay rings via Frobenius map

通过 Frobenius 贴图表征 Cohen-Macaulay 环

• 发表时间: 2004
• 期刊: Proceedings of the A. M. S. 132
• 作者: R.Takahashi;Y.Yoshino
• 通讯作者: Y.Yoshino