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We prove a global effective membership result for polynomials on anon-reduced algebraic subvariety of $\C^N$. It can be seen as a global versionof a recent local result of Sznajdman, generalizing theBrian\c{c}on-Skoda-Huneke theorem for the local ring of holomorphic functionsat a point on a reduced analytic space.

A global Brian\c{c} con-Skoda-Huneke-Sznajdman theorem