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 $p\geq 1$, 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 ${\cal D}_X$-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces $Y$ such that ${\cal L}(Y,X)$ coincides with $H^p_{[Y]}({\cal O}_X)$, in terms of Bernstein-Sato functional equations.