Stable degenerations of Cohen-Macaulay modules

TL;DR

This paper introduces the concept of stable degenerations for Cohen-Macaulay modules over Gorenstein local algebras, providing conditions to determine when one module degenerates to another, advancing understanding in module theory.

Contribution

It defines stable degenerations for Cohen-Macaulay modules and establishes necessary and sufficient conditions for such degenerations, a novel approach in the field.

Findings

Provides criteria for stable degenerations of Cohen-Macaulay modules

Establishes necessary and sufficient conditions for module degeneration

Enhances understanding of module degenerations over Gorenstein algebras

Abstract

As a stable analogue of degenerations, we introduce the notion of stable degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We shall give several necessary and/or sufficient conditions for the stable degeneration. These conditions will be helpful to see when a Cohen-Macaulay module degenerates to another.