A Vanishing Theorem and Asymptotic Regularity of Powers of Ideal Sheaves

Original · EN

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