Smooth quiver quotient varieties

TL;DR

This paper classifies all quiver and dimension vector combinations that produce smooth moduli spaces of semisimple representations, reducing them to three fundamental types through specific reduction steps.

Contribution

It provides a complete classification of smooth quiver quotient varieties, identifying the fundamental types via reduction methods.

Findings

All smooth quiver quotient varieties can be reduced to three basic types.

The classification covers all quivers with smooth semisimple representation spaces.

The reduction steps simplify the analysis of quiver moduli spaces.

Abstract

In this paper we classify all the quivers and corresponding dimension vectors having a smooth space of semisimple representation classes. The result is that these quiver settings can be reduced via some specific reduction steps to 3 simple types.