Orbit closures of directing modules are regular in codimension one

TL;DR

This paper proves that the orbit closures of directing modules are smooth in all but possibly codimension one, providing insights into specific components of module varieties.

Contribution

It establishes the regularity in codimension one of orbit closures of directing modules, a new geometric property in representation theory.

Findings

Orbit closures of directing modules are regular in codimension one.

Provides new understanding of distinguished irreducible components.

Enhances geometric understanding of module varieties.

Abstract

We show that the orbit closure of a directing module is regular in codimension one. In particular, this result gives information about a distinguished irreducible component of a module variety.