Symplectic resolutions of quiver varieties
File(s)
Author(s)
Bellamy, Gwyn
Schedler, Travis
Type
Journal Article
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.
Date Issued
2021-05-24
Date Acceptance
2020-11-29
Citation
Selecta Mathematica, 2021, 27 (36), pp.1-50
ISSN
1022-1824
Publisher
Springer
Start Page
1
End Page
50
Journal / Book Title
Selecta Mathematica
Volume
27
Issue
36
Copyright Statement
© The Author(s) 2021.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Sponsor
National Science Foundation
Identifier
https://link.springer.com/article/10.1007/s00029-021-00647-0
Grant Number
DMS-1406553
Subjects
General Mathematics
0101 Pure Mathematics
Publication Status
Published
Date Publish Online
2021-05-24