Intersection homology D-Modules 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>0, 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 D_X-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces Y such that L(Y,X) coincides with $H_{[Y]}^p({\mathcal{O}}_X)$, in terms of Bernstein-Sato functional equations.

16 pages