Intersection homology D-Modules and Bernstein polynomials associated with a complete intersection

TL;DR

This paper characterizes when the intersection homology D-module associated with a subspace Y coincides with the local algebraic cohomology sheaf on a complex manifold, using Bernstein-Sato functional equations.

Contribution

It provides an algebraic criterion for the equality of intersection homology D-modules and local cohomology sheaves based on Bernstein-Sato equations.

Findings

Characterization of Y for which L(Y,X) equals H^p_{[Y]}({ m O}_X)

Use of Bernstein-Sato functional equations for algebraic criteria

Insight into the structure of intersection homology D-modules

Abstract

Let X be a complex analytic manifold. Given a closed subspace $Y\subset X$ of pure codimension p>0, we consider the sheaf of local algebraic cohomology $H^p_{[Y]}({\cal O}_X)$, and ${\cal L}(Y,X)\subset H^p_{[Y]}({\cal O}_X)$ the intersection homology D_X-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces Y such that L(Y,X) coincides with $H^p_{[Y]}({\cal O}_X)$, in terms of Bernstein-Sato functional equations.