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We prove global effective versions of the Brian\ccon-Skoda-Huneke theorem.Our results extend, to singular varieties, a result of Hickel on the membershipproblem in polynomial ideals in $\mathbf C^n$, and a related theorem of Ein andLazarsfeld for smooth projective varieties. The proofs rely on known geometricestimates and new results on multivariable residue calculus.

Global effective versions of the Brian\ccon-Skoda-Huneke theorem