Moduli spaces of twisted sheaves on a projective variety

TL;DR

This paper constructs moduli spaces of twisted sheaves on projective varieties, generalizes known results from untwisted sheaves on K3 surfaces, and applies these to prove Caldararu's conjecture.

Contribution

It introduces the moduli of twisted sheaves on projective varieties and extends classical results to this broader context.

Findings

Established non-emptiness and deformation properties of twisted sheaf moduli

Generalized Fourier-Mukai transformations to twisted sheaves

Proved Caldararu's conjecture using these moduli spaces

Abstract

We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the Fourier-Mukai transformation. As an application of our results, Daniel Huybrechts and Paolo Stellari prove Caldararu's conjecture.