Explicit versions of the Briançon-Skoda theorem with variations

2005/03/14 by Mats Andersson, Andersson, Mats · 1 citation
Computer Science · Mathematics · #32A26 #32A27 #32B10 #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.math/0503257

openalex publication_date 2005/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give new a proof of the general Briançon-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 Briançon-Skoda theorem, with integral representation formulas.

Cited by

• The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities and uniformity in excellent rings

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