A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves

2010/09/02 by Wenbo Niu, Niu, Wenbo
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.1009.0314

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

arxiv created 2011/06/14 · arxiv updated 2011/06/15

Abstract

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

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