Decomposition of Marsden-Weinstein reductions for representations of quivers

2000/07/31 by William Crawley-Boevey · 2 citations
Mathematics · #math.AG #msc:16G20 #msc:53D20

paper · pdf

published as Compositio Math., 130 (2002), 225-239 · 12 pages; correction: the arguments do not prove reducedness of the schemes

arxiv created 2001/02/12 · arxiv updated 2009/11/30

Abstract

We decompose the Marsden-Weinstein reductions for the moment map associated to representations of a quiver. The decomposition involves symmetric products of deformations of Kleinian singularities, as well as other terms. As a corollary we deduce that the Marsden-Weinstein reductions are irreducible varieties.

Cited by

• Nakajima quiver varieties in dimension four
• The tame Deligne-Simpson problem

Related

• Decomposition of Marsden–Weinstein Reductions for Representations of Quivers
• Normality of Marsden-Weinstein reductions for representations of quivers
• Stratifications of Marsden-Weinstein reductions for representations of quivers and deformations of symplectic quotient singularities
• Geometry of the Moment Map for Representations of Quivers
• On the Reducedness of Quiver Schemes