A global Brianc{c} con-Skoda-Huneke-Sznajdman theorem

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 Brian\c{c}on-Skoda-Huneke theorem for the local ring of holomorphic functions at a point on a reduced analytic space.