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On singular Calogero-Moser spaces

Bellamy, G. (2009) On singular Calogero-Moser spaces. Bulletin of the London Mathematical Society, 41 (2). pp. 315-326. ISSN 0024-6093 (doi:10.1112/blms/bdp019)

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Abstract

Using combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter c if and only if the group is different from the wreath product $S_n\wr C_m$ and the binary tetrahedral group. This result and a theorem of Ginzburg and Kaledin imply that there does not exist a symplectic resolution of the singular symplectic variety h+h*/W outside of these cases; conversely we show that there exists a symplectic resolution for the binary tetrahedral group (Hilbert schemes provide resolutions for the wreath product case).

Item Type:Article
Status:Published
Refereed:Yes
Glasgow Author(s):Bellamy, Dr Gwyn
Authors: Bellamy, G.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Research Group:Algebra
Journal Name:Bulletin of the London Mathematical Society
Publisher:Oxford University Press
ISSN:0024-6093
Published Online:11 March 2009
Copyright Holders:Copyright © 2009 London Mathematical Society
First Published:First published in Bulletin of the London Mathematical Society 41(2):315-326
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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