Non Cohen–Macaulay locus of canonical modules.

Abstract Let (R , m) be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let M be a finitely generated R -module and K M the canonical module of M. Denote by nCM (M) the non Cohen–Macaulay locus of M. In this paper, the relationship between the two loci nCM (K M) and nCM (M) is given. The structure of M is clarified in case where dim ⁡ nCM (K M) ≤ 0 (i.e. K M is generalized Cohen–Macaulay). [ABSTRACT FROM AUTHOR]