A global Briançon-Skoda-Huneke-Sznajdman theorem

Abstract

We prove a global effective membership result for polynomials on a non-reduced algebraic subvariety of C N . It can be seen as a global version of a recent local result of Sznajdman, generalizing the Briançon-Skoda-Huneke theorem for the local ring of holomorphic functions at a point on a reduced analytic space.