On the Briancon-Skoda theorem on a singular variety

TL;DR

This paper provides an analytic proof of the uniform Briancon-Skoda theorem for reduced analytic spaces, offering sharper results for ideals with few generators, thus advancing understanding of ideal membership in singular varieties.

Contribution

It offers an analytic proof of the Briancon-Skoda theorem on singular varieties, complementing algebraic proofs and improving results for ideals with few generators.

Findings

Analytic proof of the uniform Briancon-Skoda theorem for reduced analytic spaces.

Sharper results obtained for ideals with few generators.

Extension of the theorem's applicability to singular varieties.

Abstract

Let $Z$ be a germ of a reduced analytic space of pure dimension. We provide an analytic proof of the uniform Briancon-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.