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Multi-Gieseker semistability and moduli of quiver sheaves

Authors
  • Maslovarić, Marcel
  • Seppänen, Henrik
Type
Published Article
Journal
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Publisher
Springer Berlin Heidelberg
Publication Date
Sep 07, 2018
Volume
60
Issue
2
Pages
257–332
Identifiers
DOI: 10.1007/s13366-018-0417-3
Source
Springer Nature
Keywords
License
Yellow

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.

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