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.

在代数分析的背景下，我们研究了附着在零维准素理想上的Noether算子，相关的代数局部上同调和Grothendieck对偶。本文研究了附着在拟齐次孤立奇点上的完整D-模的结构。1.引入了附着在零维准素理想上的Noether算子的概念。阐明了它们的基本性质。一种计算Noether算子基的算法。2.构造了一个计算引导零维代数局部上同调类的完整D-模的算法。一种计算对偶基w.r.t.构造了Grothendieck对偶; 4.给出了计算Grothendieck局部剩余的新方法; 5.考虑了内模至多为4的半拟齐次孤立奇点。研究了这些奇点上的完整D-模。通过实例计算证明了这类完整系统的重数等于Milnor数与Tjurina数之差的事实，并研究了附加在高维准理想和剩余流上的Noether算子.

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

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。

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）。

Unimodal singularities and diffeential operators

单峰奇点和微分算子

• 期刊: Seminaires et Congres, Singularitees Franco-Japonaise, Societe Mathematiques de France (印刷中)
• 作者: Shuichi Sato;田島慎一;KAWAMURA Shinzo;S.Tajima;S.Tajima;S.Tajima;Y.Nakamura
• 通讯作者: Y.Nakamura

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)。