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 ⊂ X of pure codimension p ≥ 1, we consider the sheaf of local algebraic cohomology H pY ] (OX), and L(Y,X) ⊂ H p [Y ](OX) the intersection homology DX-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces Y such that L(Y,X) coincides with H p [Y ] (OX), in terms of Bernstein-Sato functional equations.