Regularity of powers of cover ideals of unimodular hypergraphs

摘要

Let H be a unimodular hypergraph over the vertex set [n] and let J(H) be the cover ideal of H in the polynomial ring R = K [x(1),..., x(n)]. We show that reg J(H)(s) is a linear function in s for all s = r[n/2] + 1 where r is the rank of H. Moreover for every i, a(i) (R/J(H)(s)) is also a linear function in s for s = n(2) . (C) 2018 Elsevier Inc. All rights reserved.