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On the equations and classification of toric quiver varieties

Published online by Cambridge University Press:  03 March 2016

Mátyás Domokos
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13–15, 1053 Budapest, Hungary and Department of Mathematics, Central European University, Nádor utca 9, 1051 Budapest, Hungary ([email protected]; [email protected])
Dániel Joó
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda utca 13–15, 1053 Budapest, Hungary and Department of Mathematics, Central European University, Nádor utca 9, 1051 Budapest, Hungary ([email protected]; [email protected])

Abstract

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight, there is an associated quasi-projective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with no oriented cycles the homogeneous ideal of this embedded projective variety is generated by elements of degree at most 3. In each fixed dimension d up to isomorphism there are only finitely many d-dimensional toric quiver varieties. A procedure for their classification is outlined.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2016 

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