A remark on symbolic powers
Tom 249 / 2019
Streszczenie
The symbolic powers of an ideal {\mathcal I}\subset {\mathcal {O}}(X) generated by holomorphic functions g_1,\ldots ,g_r\in {\mathcal {O}}(Y) on a Stein manifold X\Subset Y are shown to satisfy {\mathcal I}^{(p+q)}\subset {\mathcal I}^p for q=\min\{\dim X,r-1\} and all p\in {\mathbb N}, which contributes to the so-called containment problem. In particular, this is true if {\mathcal I} is the vanishing ideal of a finite set.