Ulrich modules over cyclic quotient surface singularities

TL;DR

This paper characterizes Ulrich modules over cyclic quotient surface singularities using special Cohen-Macaulay modules and relates their number to the geometry of the minimal resolution.

Contribution

It provides a characterization of Ulrich modules in this setting and establishes a bound on their number based on the minimal resolution's exceptional curves.

Findings

Ulrich modules are characterized via special Cohen-Macaulay modules.

The number of indecomposable Ulrich modules is bounded by the number of exceptional curves.

A relationship between the geometry of the singularity and Ulrich modules is established.

Abstract

In this paper, we characterize Ulrich modules over cyclic quotient surface singularities by using the notion of special Cohen-Macaulay modules. We also investigate the number of indecomposable Ulrich modules for a given cyclic quotient surface singularity, and show that the number of exceptional curves in the minimal resolution gives a boundary for the number of indecomposable Ulrich modules.