On the self-dual maximal Cohen-Macaulay modules

Abstract

We study the duality for maximal Cohen-Macaulay modules (MCM modules for short) over Cohen-Macaulay local rings. We characterize (low dimensional) rings over which any MCM module is self-dual, and establish a correspondence between the isomorphism classes of a class of self-dual MCM modules (called “orientable” Auslander modules) and the even linkage classes of Gorenstein ideals of height two over Gorenstein normal domains. An application is given to the complete intersection ideals of height two.