On orbit closures for infinite type quivers

TL;DR

This paper extends Zwara's example of a representation with a non-unibranch, non-Cohen-Macaulay orbit closure from the Kronecker quiver to all infinite type quivers without oriented cycles, highlighting complex geometric properties.

Contribution

It generalizes Zwara's specific example to a broad class of infinite type quivers, revealing new geometric phenomena in their orbit closures.

Findings

Orbit closures are neither unibranch nor Cohen-Macaulay for all infinite type quivers without cycles.

The geometric complexity observed in the Kronecker quiver extends to a wider class of quivers.

The results deepen understanding of the singularities in quiver representation varieties.

Abstract

For the Kronecker quiver, Zwara has found an example of a representation whose orbit closure is neither unibranch nor Cohen-Macaulay. In this note, we explain how to extend this example to all infinite type quivers without oriented cycles.