Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T12:48:09.010Z Has data issue: false hasContentIssue false
  • English
  • Français

On the equations and classification of toric quiver varieties

Part of: Algebraic groups Special varieties Polytopes and polyhedra Representation theory of rings and algebras

Published online by Cambridge University Press:  03 March 2016

Mátyás Domokos  and
Dániel Joó
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 (domokos.matyas@renyi.mta.hu; joo.daniel@renyi.mta.hu)
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 (domokos.matyas@renyi.mta.hu; joo.daniel@renyi.mta.hu)
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

binomial idealquiver representationmoduli spaceflow polytope

MSC classification

Primary: 14M25: Toric varieties, Newton polyhedra
Secondary: 14L24: Geometric invariant theory 16G20: Representations of quivers and partially ordered sets 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 265 - 295
Copyright
Copyright © Royal Society of Edinburgh 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)