Regularity of powers of cover ideals of unimodular hypergraphs

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[x1,…,xn]. We show that regJ(H)s is a linear function in s for all s⩾r⌈n2⌉+1 where r is the rank of H. Moreover for every i, ai(R/J(H)s) is also a linear function in s for s⩾n2.