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

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.