Normality of Marsden-Weinstein reductions for representations of quivers

By W. Crawley‐Boevey. 2001

97 citations recorded by the source corpus.

Abstract. We prove that the Marsden-Weinstein reductions for the moment map associated to representations of a quiver are normal varieties. We give an application to conjugacy classes of matrices.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fd6c5ec1291c7e117fa056be05bc92f98518670c

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quantum Groups and Quantum Cohomology (2012, background): “s on the geometry of Nakajima quiver varieties. There is a large literature on the subject, although most of what we need can be found in the original references [84, 87] and papers of Crawley-Boevey [21, 22]. We also explain some results on natural group actions on Nakajima quiver varieties. 2.1 De”
Quiver varieties and cluster algebras (2009, methodology): “We decompose it into a sum of indecomposable representations.”
On cohomological Hall algebras of quivers: Generators (2017, background): “We’ll assume that the reader is familiar with the formalism of quiver varieties and we’ll refer to [8], [9], [29], [30], [31], [32], [33] for the proofs of the facts recalled below.”
Instanton counting on blowup. II. K-theoretic partition function (2005, background): “It is known that M0(r, n) is a normal variety by [3].”
Isomorphisms of quantizations via quantization of resolutions (2010, methodology): “braic variety to be referred to as a (universal) aﬃne quiver variety. Also we can form the reductions Mχ(DQ,v,d),MU(DQ,v,d). These reductions were studied by Crawley-Boevey, see, in particular, [CB1],[CB2]. In fact, he worked only with the case when d = 0. However, the general case can be reduced to”