Degenerations over $(A_\infty)$-singularities and construction of degenerations over commutative rings

TL;DR

This paper investigates conditions for module degenerations over $A_ abla$-singularities, focusing on Cohen-Macaulay modules, and introduces a method to construct degenerations over commutative rings.

Contribution

It provides a necessary condition for degenerations via matrix representations and a new method for constructing degenerations over commutative rings.

Findings

Derived a necessary condition for module degeneration

Analyzed degenerations of Cohen-Macaulay modules over hypersurface singularities

Proposed a construction method for degenerations over commutative rings

Abstract

We give a necessary condition of degeneration via matrix representations, and consider degenerations of indecomposable Cohen-Macaulay modules over hypersurface singularities of type ($A_\infty$). We also provide a method to construct degenerations of finitely generated modules over commutative rings.