On the Briançon-Skoda theorem on a singular variety

[Sur le théorème de Briançon-Skoda sur une variété singulière]

Andersson, Mats ; Samuelsson, Håkan ; Sznajdman, Jacob

Annales de l'Institut Fourier, Tome 60 (2010), p. 417-432 / Harvested from Numdam

Résumé

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 $\mathcal{O}_Z$. 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.

Abstract

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 $\mathcal{O}_Z$; a result which was previously proved by Huneke by algebraic methods. For ideals with few generators we also get much sharper results.

Détail

Publié le : 2010-01-01

MR 2667781 | Zbl 1200.32007 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2527
Classification:  32C30,  32A27,  13A05
Mots clés: théorème de Briançon-Skoda, espace analytique, courant résiduel

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