A remark on symbolic powers

15 Feb 2018 Rashkovskii Alexander

Let an ideal $I$ of holomorphic functions on an $n$-dimensional Stein manifold $X$ be generated by $r$ functions holomorphic on a neighbourhood of $\overline X$. By an easy application of Skoda's theorem on ideal generation, we show that symbolic powers $I^{(p)}$ of $I$ satisfy $I^{(p+q)} \subset I^p$ for $q=\min\{n, r-1\}$ and all natural $p$...

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