Global effective versions of the Briançon–Skoda–Huneke theorem

Abstract

We prove global effective versions of the Briancon–Skoda–Huneke theorem. Our results extend, to singular varieties, a result of Hickel on the membership problem in polynomial ideals in Cn, and a related theorem of Ein and Lazarsfeld for smooth projective varieties. The proofs rely on known geometric estimates and new results on multivariable residue calculus.