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Fano quiver moduli

Part of:Families, fibrationsSurfaces and higher-dimensional varietiesRepresentation theory of rings and algebras

Published online by Cambridge University Press:  28 December 2020

Hans Franzen,
Markus Reineke and
Silvia Sabatini
Hans Franzen
Affiliation:
Faculty of Mathematics, Ruhr-University Bochum, Universitätsstrasse 150, 44780 Bochum, Germany e-mail: hans.franzen@rub.de
Markus Reineke*
Affiliation:
Faculty of Mathematics, Ruhr-University Bochum, Universitätsstrasse 150, 44780 Bochum, Germany e-mail: hans.franzen@rub.de
Silvia Sabatini
Affiliation:
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany e-mail: sabatini@math.uni-koeln.de
*
e-mail: Markus.Reineke@ruhr-uni-bochum.de
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Abstract

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We exhibit a large class of quiver moduli spaces, which are Fano varieties, by studying line bundles on quiver moduli and their global sections in general, and work out several classes of examples, comprising moduli spaces of point configurations, Kronecker moduli, and toric quiver moduli.

Keywords

Quiver representationsquiver moduli spacesFano varieties

MSC classification

Primary:16G20: Representations of quivers and partially ordered sets
Secondary:14D20: Algebraic moduli problems, moduli of vector bundles14J45: Fano varieties

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021, pp. 984 - 1000
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Copyright
© Canadian Mathematical Bulletin 2020

Footnotes

The authors are supported by the DFG SFB/Transregio 191 “Symplektische Strukturen in Geometrie, Algebra, und Dynamik.” The second-named author is supported by the DFG GRK 2240 “Algebro-Geometrische Methoden in Algebra, Arithmetik, und Topologie.”

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