RIGIDITY AND SCHOFIELD’S PARTIAL TILTING CONJECTURE FOR QUIVER MODULI

Abstract

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