On the Briançon-Skoda theorem on a singular variety

Andersson, Mats; Samuelsson, Håkan; Sznajdman, Jacob

Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 417-432.

Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briançon-Skoda theorem for the local ring ${𝒪}_Z$; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

Soit $Z$ un germe d’un espace analytique réduit de dimension pure. Nous donnons une démonstration analytique du théorème de Briançon-Skoda pour l’anneau local ${𝒪}_Z$. Ce résultat a déjà été démontré par Huneke en utilisant des méthodes algébriques. Nous obtenons également un résultat beaucoup plus fort pour les idéaux engendrés par peu d’éléments.

Classification: 32C30, 32A27, 13A05
Keywords: Briançon-Skoda theorem, analytic space, residue current
Mot clés : théorème de Briançon-Skoda, espace analytique, courant résiduel

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