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

在代数分析的背景下，我们研究了零维素理想上的Noether算子，以及相应的代数局部上同调和Grothendieck对偶。我们研究了附着于拟齐次孤立奇点的完整D-模的结构。1.引入了附着于零维初等理想的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。构造了一个计算零维代数局部上同调类的完整D-模的算法。3.研究了Hermite-Jacobi再生核。一种计算对偶基的方法。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的半齐次孤立奇点.研究了附加在这些奇点上的完整D-模。通过实例计算证明了这类完整系统的重数等于Milnor数和Tjuina数之差，并研究了高维原始理想和残余流的Noether算子。

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.