Symplectic resolutions of quiver varieties

Bellamy, G. and Schedler, T. (2021) Symplectic resolutions of quiver varieties. Selecta Mathematica, 27(3), 36. (doi: 10.1007/s00029-021-00647-0)

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In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically θ-polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., and Schedler, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Selecta Mathematica
ISSN (Online):1420-9020
Published Online:24 May 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Selecta Mathematics 27(3): 36
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
171924Symplectic representation theoryGwyn BellamyEngineering and Physical Sciences Research Council (EPSRC)EP/N005058/1M&S - Mathematics