A remark on symbolic powers

Alexander Rashkovskii

arXiv:1802.02027·math.CV·February 2, 2021

A remark on symbolic powers

Alexander Rashkovskii

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Abstract

By an easy application of Skoda's theorem on ideal generation, a non-local version of the Briancon-Skoda theorem is obtained. In particular, the symbolic powers $I^{(p)}$ of a zero dimensional radical ideal $I$ generated by $r$ holomorphic functions on an $n$ -dimensional Stein manifold are shown to satisfy $I^{(p + q)} \subset I^{p}$ for $q = min {n, r - 1}$ and all natural $p$ , which contributes to the so-called containment problem.

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