Mathematical Proceedings of the Cambridge Philosophical Society

Bass numbers of local cohomology modules with supports in monomial ideals

a1 Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan. e-mail:


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 Extnd(S/I, [fraktur w]S) is Cohen–Macaulay), we can ‘visualize’ a [open face Z]n-graded minimal injective resolution of HndI(S) using Stanley–Reisner's simplicial complex of I.

(Received November 1 1999)
(Revised April 12 2000)