On linear resolution of powers of an ideal

Abstract

In this paper we give a generalization of a result of Herzog, Hibi, and Zheng providing an upper bound for regularity of powers of an ideal. As the main result of the paper, we give a simple criterion in terms of Rees algebra of a given ideal to show that high enough powers of this ideal have linear resolution. We apply the criterion to two important ideals $J,J_1$ for which we show that $J^k,$ and $J_1^k$ have linear resolution if and only if $k\ne 2.$ The procedures we include in this work is encoded in computer algebra package CoCoA.

10 pages, to appear in Osaka Journal of Mathematics

References in corpus (1)

• Castelnuovo-Mumford regularity of products of ideals