Localization, local cohomology, and the b-function of a D-module with respect to a polynomial

2016/09/15 by Oaku, Toshinori
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.04676

Abstract

Given a D-module M generated by a single element, and a polynomial f, one can construct several D-modules attached to M and f and can define the notion of the (generalized) b-function following M. Kashiwara. These modules are closely related to the localization and the local cohomology of M. We show that the b-function, if it exists, controls these modules and present general algorithms for computing these modules and the b-function (if it exists) without any further assumptions. For these algorithms, we reformulate the localization algorithm for D-modules.

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