On the (non)existence of symplectic resolutions of linear quotients

Bellamy, G. and Schedler, T. (2016) On the (non)existence of symplectic resolutions of linear quotients. Mathematical Research Letters, 23(6), pp. 1537-1564. (doi:10.4310/MRL.2016.v23.n6.a1)

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Abstract

We study the existence of symplectic resolutions of quotient singularities V/GV/G, where VV is a symplectic vector space and GG acts symplectically. Namely, we classify the symplectically irreducible and imprimitive groups, excluding those of the form K⋊S2K⋊S2 where K<SL2(C)K<SL2(C), for which the corresponding quotient singularity admits a projective symplectic resolution. As a consequence, for dimV≠4dim⁡V≠4, we classify all symplectically irreducible quotient singularities V/GV/G admitting a projective symplectic resolution, except for at most four explicit singularities, that occur in dimensions at most 1010, for which the question of existence remains open.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G., and Schedler, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematical Research Letters
Publisher:International Press
ISSN:1073-2780
ISSN (Online):1945-001X
Copyright Holders:Copyright © 2016 International Press
First Published:First published in Mathematical Research Letters 23(6):1537-1564
Publisher Policy:Reproduced with the permission of the publisher.

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
620601Geometric methods in representation theory of rational Cherednik algebrasGwyn BellamyEngineering & Physical Sciences Research Council (EPSRC)EP/H028153/1M&S - MATHEMATICS