Mathematical Proceedings of the Cambridge Philosophical Society



Bass numbers of local cohomology modules with supports in monomial ideals


KOHJI YANAGAWA a1
a1 Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan. e-mail: yanagawa@math.sci.osaka-u.ac.jp

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 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)