Explicit versions of the Briancon-Skoda theorem with variations
Abstract
We give new a proof of the general Briancon-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a related result for the ideal generated by the the subdeterminants of a matrix-valued generically surjective holomorphic function, generalizing the duality theorem for a complete intersection. We also provide explicit versions of the various results, including the general Briancon-Skoda theorem, with integral representation formulas.
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