Properness of moment maps for representations of quivers

2017/12/04 by Das, Pradeep
#16G20 #53D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1712.00934

Abstract

In this note, we give a necessary and sufficient condition for the properness of moment maps for representations of quivers. We show that the moment map for the representations of a quiver is proper if and only if the quiver is acyclic, that is, it does not contain any oriented cycle.

Related

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• Moment map flows and the Hecke correspondence for quivers
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• Decomposition of Marsden-Weinstein reductions for representations of quivers
• Morse theory of the moment map for representations of quivers