Algebraic Analysis of residue currents and an algorithm for computing Noether operators

剩余电流的代数分析和诺特算子的计算算法

• 批准号: 15540159
• 负责人: TAJIMA Shinichi
• 金额: $ 1.54万
• 依托单位: Niigata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540159/
• 关键词: Noetherian; holonomic system; Residue; Hermite-Jacobi reproducing kernel; Grothendieck duality; Milnor number; Tjurina namber; グロタンディエック双対性; ミルナー数; チュリナ数

We have investigated Noether operators attached to a zero-dimensional primary ideal, the associated algebraic local cohomology and Grothendieck duality in the context of algebraic analysis. We have studies the structure of holonomic D-modules attached to a quasi-Homogeneous isolated singularity.1.A concept of Noether operators attaced to a zero-dimensional primary ideal is introduced. Their fundamental properties are clarified. An algorithm that compute Noether operator basis. are derived.2.An algorithm for computing holonomic D-module that leads zero-dimensional algebraic local cohomology class is constructed.3.Hermite-Jacobi reproducing kernel is investigated. A method for computing dual basis w.r.t. Grothendieck duality is constructed.4.A new method that compute Grothendieck local residue is derived.5.Semi quasi-homogeneous isolated singularities with inner modarity (at most) four are considered. Holonomic D-modules attached to these singularities are investigated. The factthat he multiplicity of such holonomic system is equal to the difference of Milnor number and Tjurina namber has proved by case by case computation.Besides, we have investigated Noether operator attaced to higher dimensional primary ideal and residue currents.

我们已经调查了与零维主要理想相关的noether运算符，在代数分析的背景下，相关的代数局部共同体学和Grothendieck二元性。我们研究了与准均匀分离的奇异性相连的载体D模块的结构。1。引入了与零维主要理想的Noether操作员的概念。他们的基本属性被阐明。计算Noether操作员基础的算法。 2.用于计算载体D模块的算法，该算法构建了零维代数局部共同体学类别。3.Hermite-Jacobi重现内核。计算双重基础W.R.T.的方法4.一种新的方法，一种计算Grothendieck局部残基的新方法。5.Semi准二均匀的分离奇异性具有内在性（最多）四种。研究了与这些奇异性相关的自动型D模块。这种自动系统的多样性等于Milnor数量的差异，而Tjurina Namber已按照案例计算证明。Besides，我们已经调查了与较高尺寸的原发性理想和残余电流相关的noether操作员。

项目成果

Inhomogeneous ordinary differential equations, local cohomology, And residues

非齐次常微分方程、局部上同调和留数

• 发表时间: 2003
• 期刊: Finite and Infinite Dimensional Complex Analysis and Applications
• 作者: AIHARA Yoshihiro;MORI Seiki;Shuichi Sato;S.Tajima
• 通讯作者: S.Tajima

Y.Nakamura, S.Tajima: "Unimodal singularities and differential operators"Seminaires et Congres, Singularites Franco-Japonaise, Societes Matheinatiques de France. (印刷中).

Y.Nakamura、S.Tajima：“单峰奇点和微分算子”研讨会和会议，Singularites Franco-Japonaise，Societes Matheinatiques de France（正在出版）。

S.Tajima: "Inhomogeneous ordinary differential equations, local cohomologies and residues"Finite and Infinite Dimensional Complex Analysis. 361-370 (2003)

S.Tajima：“非齐次常微分方程、局部上同调和留数”有限和无限维复分析。

Algebraic local cohomology classes attached to quasi-Homogeneous isolated singularities

附属于准齐次孤立奇点的代数局部上同调类

• 发表时间: 2005
• 期刊: Publ.Res.Inst.Math.Sci. 41
• 作者: MAJIMA;Hideyuki;真島秀行;S.Tajima
• 通讯作者: S.Tajima

田島慎一, 中村弥生: "Hermite-Jacobi再生核の計算代数解析"京都大学数理解析研究所講究録. 1352. 1-10 (2004)

Shinichi Tajima、Yayoi Nakamura：“Hermite-Jacobi 再生核的计算代数分析”京都大学数学分析研究所 Kokyuroku 1352. 1-10 (2004)。