On regularity in codimension one of irreducible components of module varieties

TL;DR

This paper proves that for tame quasi-tilted algebras, the irreducible components of module varieties corresponding to indecomposable modules are regular in codimension one, revealing geometric regularity properties.

Contribution

It establishes a new regularity result in the geometry of module varieties for a class of tame algebras, specifically in codimension one.

Findings

Irreducible components are regular in codimension one

Applicable to modules over tame quasi-tilted algebras

Advances understanding of module variety geometry

Abstract

Let A be a tame quasi-tilted algebra and d the dimension vector of an indecomposable A-module. In the paper we prove that each irreducible component of the variety of A-modules of dimension vector d is regular in codimension one.