Osaka Journal of Mathematics

On linear resolution of powers of an ideal

Keivan Borna

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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 [3].

Article information

Osaka J. Math., Volume 46, Number 4 (2009), 1047-1058.

First available in Project Euclid: 15 December 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D02: Syzygies, resolutions, complexes
Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)


Borna, Keivan. On linear resolution of powers of an ideal. Osaka J. Math. 46 (2009), no. 4, 1047--1058.

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