Rigidity and Schofield's partial tilting conjecture for quiver moduli

TL;DR

This paper applies Teleman quantization to quiver moduli spaces to compute cohomology, proving Schofield's partial tilting conjecture and demonstrating the infinitesimal rigidity of these moduli spaces.

Contribution

It introduces a novel application of Teleman quantization to quiver moduli, proving a longstanding conjecture and establishing rigidity results.

Findings

Proved Schofield's partial tilting conjecture

Computed higher cohomology of endomorphism bundles

Established infinitesimal rigidity of quiver moduli spaces

Abstract

We explain how Teleman quantization can be applied to moduli spaces of quiver representations to compute the higher cohomology of the endomorphism bundle of the universal bundle. We use this to prove Schofield's partial tilting conjecture, and to show that moduli spaces of quiver representations are (infinitesimally) rigid as varieties.