Some new examples of non-degenerate quiver potentials

TL;DR

This paper introduces a new technical result that demonstrates the non-degeneracy of certain quiver potentials, expanding understanding in specific algebraic and geometric contexts.

Contribution

It provides a novel method to prove non-degeneracy of quiver potentials in cases involving McKay quivers and geometric helices on Del Pezzo surfaces.

Findings

Established non-degeneracy for specific McKay quivers

Proved non-degeneracy for potentials from geometric helices on Del Pezzo surfaces

Extended the class of quivers with known non-degenerate potentials

Abstract

We prove a technical result which allows us to establish the non-degeneracy of potentials on quivers in some previously unknown or non-obvious cases. Our result applies to certain McKay quivers and also to potentials derived from geometric helices on Del Pezzo surfaces.