Normality of maximal orbit closures for Euclidean quivers

TL;DR

This paper proves that the closures of maximal orbits in Euclidean quiver representation varieties are normal and Cohen-Macaulay, and extends the result to tame concealed-canonical algebras.

Contribution

It establishes the normality and Cohen-Macaulay property of maximal orbit closures for Euclidean quivers and generalizes to tame concealed-canonical algebras.

Findings

Maximal orbit closures are normal and Cohen-Macaulay.

Results extend to tame concealed-canonical algebras.

Provides geometric properties of orbit closures in representation varieties.

Abstract

Let Delta be an Euclidean quiver. We prove that the closures of the maximal orbits in the varieties of representations of Delta are normal and Cohen--Macaulay (even complete intersections). Moreover, we give a generalization of this result for the tame concealed-canonical algebras.