Cohen-Macaulay modules over the plane curve singularity of type $T_{36}$

TL;DR

This paper explicitly describes Cohen-Macaulay modules over the local ring of a specific plane curve singularity using matrix factorizations and representation theory techniques.

Contribution

It provides an explicit classification of Cohen-Macaulay modules over the $T_{36}$ singularity via matrix factorizations and matrix problem methods.

Findings

Explicit matrix factorizations for Cohen-Macaulay modules over $T_{36}$

Application of matrix problem techniques to singularity modules

Enhanced understanding of module structure over complex plane curve singularities

Abstract

For a wide class of Cohen--Macaulay modules over the local ring of the plane curve singularity of type $T_{36}$ we describe explicitly the corresponding matrix factorizations. The calculations are based on the technique of matrix problems, in particular, representations of bunches of chains.