Bellamy, G. (2009) On singular Calogero-Moser spaces. Bulletin of the London Mathematical Society, 41(2), pp. 315-326. (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: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Bellamy, Professor 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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