GIT-cones and quivers

TL;DR

This paper advances the understanding of GIT-cones related to reductive group actions on projective varieties and applies these results to provide a concise proof of a theorem linking quiver theory and rational cones.

Contribution

It improves existing results on GIT-cones and offers a new, streamlined proof of Derksen-Weyman's Theorem for quivers without oriented cycles.

Findings

Enhanced characterization of GIT-cones for reductive group actions

A simplified proof of Derksen-Weyman's Theorem

Bijective correspondence between faces of a rational cone and quiver properties

Abstract

In this work, we improve results about GIT-cones associated to the action of any reductive group $G$ on a projective variety $X$. These results are applied to give a short proof of a Derksen-Weyman's Theorem which parametrizes bijectively the faces of a rational cone associated to any quiver without oriented cycle.