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 |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Bellamy, Professor 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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