On the effective membership problem on singular varieties

Details On the effective membership problem on singular varieties On the effective membership problem on singular varieties

2011-07-02

arxiv.org/abs/1107.0388v2

Mathematics

Complex Variables

34 pages

Scientific paper

We present some extensions to singular varieties of effective membership results previously known in $\C^n$ or smooth varieties. In particular, we extend a geometric effective Nullstellensatz due to Ein and Lazarsfeld, and a closely related result of Hickel for polynomial ideals on $\C^n$, to singular varieties. These results can be seen as global effective versions of the Brian\c{c}on-Skoda-Huneke theorem. We also have extensions to singular varieties of classical theorems of Max Noether and Macaulay.

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