Regularity of powers of quadratic sequences with applications to binomial ideals

[摘要] In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms of the regularity of its related ideals and degrees of its generators. As a consequence, we compute upper bounds for the regularity of powers of several binomial ideals. We generalize a result of Matsuda and Murai to show that the regularity of J(G)(s) is bounded below by 2s + l(G) - 1 for all s >= 1, where J(G) denotes the binomial edge ideal of a graph G and l(G) is the length of a longest induced path in G. We compute the regularity of powers of binomial edge ideals of cycle graphs, star graphs, and balloon graphs explicitly. Also, we give sharp bounds for the regularity of powers of almost complete intersection binomial edge ideals and parity binomial edge ideals. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-15

[关键词] Quadratic sequence;Related ideal;Binomial edge ideal;Castelnuovo-Mumford regularity d-sequence