On presente une etude systematique des varietes caracteristiques des systemes holonomes a singularites regulieres. Ce sont des sous-varietes lagrangiennes coniques dans le fibre cotangent T * X

Characteristic varieties and vanishing cycles.

This book presents algorithmic tools for algebraic geometry and experimental applications of them It also introduces a software system in which the tools have been implemented and with which the experiments can be carried out Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications The reader of this book will encounter Macaulay 2 in the context of concrete applications and practical computations in algebraic geometry The expositions of the algorithmic tools presented here are designed to serve as a useful guide for those wishing to bring such tools to bear on their own problems These expositions will be valuable to both the users of other programs similar to Macaulay 2 (for example, Singular and CoCoA) and those who are not interested in explicit machine computations at all The first part of the book is primarily concerned with introducing Macaulay2, whereas the second part emphasizes the mathematics

Computations in Algebraic Geometry with Macaulay 2

The purpose of this paper is to introduce a-functions and b-functions of prehomogeneous vector spaces in the original way of M. Sato and give a proof of the structure theorem of them. All the results were obtained by M. Sato when he constructed the theory of prehomogeneous vector spaces in 60’s. However he did not write a paper on his outcomes at that time. His theory was distributed through his lectures and informal seminars. Only small number of people could know it. The only publication left for us is a mimeographed note of his lecture [Sa-Sh1] written by T. Shintani in Japanese.

/pdf/theory-of-prehomogeneous-vector-spaces-algebraic-part-the-46iplazuvw.pdf

Theory of prehomogeneous vector spaces (algebraic part)—the English translation of Sato’s lecture from Shintani’s note

https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/60939/1/0983-10.pdf

Algorithms forb-Functions, Restrictions, and Algebraic Local Cohomology Groups ofD-Modules

/pdf/the-b-functions-and-holonomy-diagrams-of-irreducible-regular-p2p1ih2o9g.pdf

T. Kimura

Papers

Micro-local analysis of prehomogeneous vector spaces