Intersection Homology $\mathcal{D}$-Module and Bernstein Polynomials Associated with a Complete Intersection

Abstract

Let $X$ be a complex analytic manifold. Given a closed subspace $Y\subset X$ of pure codimension $p\ge 1$, we consider the sheaf of local algebraic cohomology $H_{[Y]}^p({\mathcal{O}}_X)$, and $\mathcal{L}(Y,X)\subset H_{[Y]}^p({\mathcal{O}}_X)$ the intersection homology ${\mathcal{D}}_X$-Module of Brylinski–Kashiwara. We give here an algebraic characterization of the spaces $Y$ such that $\mathcal{L}(Y,X)$ coincides with $H_{[Y]}^p({\mathcal{O}}_X)$, in terms of Bernstein–Sato functional equations.