On linear resolution of powers of an ideal

Details On linear resolution of powers of an ideal On linear resolution of powers of an ideal

2008-10-06

arxiv.org/abs/0810.1017v2

Mathematics

Commutative Algebra

10 pages, to appear in Osaka Journal of Mathematics

Scientific paper

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 $k\neq 2.$ The procedures we include in this work is encoded in computer algebra package CoCoA.

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