On the stable hom relation and stable degenerations of Cohen-Macaulay modules

TL;DR

This paper investigates the stable hom relation among Cohen-Macaulay modules over Gorenstein local algebras, establishing conditions for it to be a partial order and describing stable degenerations over simple singularities.

Contribution

It provides a sufficient condition for the stable hom relation to be a partial order and characterizes stable degenerations in specific singularity cases.

Findings

Stable hom relation becomes a partial order under certain conditions.

Describes stable degenerations over simple singularities.

Offers a framework for understanding Cohen-Macaulay modules in this context.

Abstract

We study the stable hom relation for Cohen-Macaulay modules over Gorenstein local algebras. We give the sufficient condition to make the stable hom relation a partial order when the base algebra is of finite representation type. As an application, we give the description of stable degenerations of Cohen-Macaulay modules over simple singularities of several types by using the stable hom relation.