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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Springer
• ISSN: 1022-1824
• 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

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
171924		Symplectic representation theory	Gwyn Bellamy	Engineering and Physical Sciences Research Council (EPSRC)	EP/N005058/1	M&S - Mathematics