Bass numbers of local cohomology modules with supports in monomial ideals

Abstract

In this paper, we will study the local cohomology modules HiI(S) of a polynomial ring S = k[x1, …, xn] with supports in a (radical) monomial ideal I. When S/I is a Cohen–Macaulay ring of dimension d (more generally, if Extn−d(S/I, [wfr ]S) is Cohen–Macaulay), we can ‘visualize’ a ℤn-graded minimal injective resolution of Hn−dI(S) using Stanley–Reisner's simplicial complex of I.