Counting resolutions of symplectic quotient singularities

Bellamy, G. (2016) Counting resolutions of symplectic quotient singularities. Compositio Mathematica, 152(1), pp. 99-114. (doi:10.1112/S0010437X15007630)

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Abstract

Let Γ be a finite subgroup of Sp(V). In this article we count the number of symplectic resolutions admitted by the quotient singularity V/Γ. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero–Moser space. In this way, we give a simple formula for the number of Q-factorial terminalizations admitted by the symplectic quotient singularity in terms of the dimension of a certain Orlik–Solomon algebra naturally associated to the Calogero–Moser deformation. This dimension is explicitly calculated for all groups Γ for which it is known that V/Γ admits a symplectic resolution. As a consequence of our results, we confirm a conjecture of Ginzburg and Kaledin.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Compositio Mathematica
Publisher:London Mathematical Society
ISSN:0010-437X
ISSN (Online):1570-5846
Copyright Holders:Copyright © 2015 London Mathematical Society
First Published:First published in Compositio Mathematica 2015 152(1):99-114
Publisher Policy:Reproduced in accordance with the copyright policy 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