A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves

Abstract

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

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

Cited by in corpus (1)

• Some Results on Asymptotic Regularity of Ideal Sheaves