Orbit closures of representations of source-sink Dynkin quivers

TL;DR

This paper employs geometric techniques to compute resolutions of orbit closures in source-sink Dynkin quivers, establishing their normality and extending results to certain E-type orbit closures.

Contribution

It introduces a method to explicitly resolve orbit closures in source-sink Dynkin quivers and proves their normality, including new cases in E-type quivers.

Findings

Resolved orbit closures explicitly using Weyman's geometric technique

Proved normality of orbit closures in source-sink Dynkin quivers

Extended normality results to certain E-type orbit closures

Abstract

We use the geometric technique, developed by Weyman, to calculate the resolution of orbit closures of representations of Dynkin quivers with every vertex being source or sink. We use this resolution to derive the normality of such orbit closures. As a consequence we obtain the normality of certain orbit closures of type E.