A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves

Details A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves

2010-09-02

arxiv.org/abs/1009.0314v3

Mathematics

Algebraic Geometry

13 pages; Corrected typos, added references, improve one of the main theorems

Scientific paper

Let $\mathscr{I}$ be an ideal sheaf on $P^n$. In the first part of this paper, we bound the asymptotic regularity of powers of $\mathscr{I}$ as $ps-3\leq \reg \mathscr{I}^p\leq ps+e$, where $e$ is a constant and $s$ is the $s$-invariant of $\mathscr{I}$. We also give the same upper bound for the asymptotic regularity of symbolic powers of $\mathscr{I}$ under some conditions. In the second part, by using multiplier ideal sheaves, we give a vanishing theorem of powers of $\mathscr{I}$ when it defines a local complete intersection subvariety with log canonical singularities.

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