Multi-Gieseker semistability and moduli of quiver sheaves

Abstract

We generalize the notion of multi-Gieseker semistability for coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves using a functorial method that realizes these as subschemes of moduli spaces of representations of a twisted quiver, depending on Q, with relations. We also show the projectivity of the moduli space in the case when Q has no oriented cycles. Further, we construct moduli spaces of quiver sheaves which satisfy a given set of relations as closed subvarieties. Finally, we investigate the parameter dependence of the moduli.