On singular Calogero-Moser spaces

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

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
• 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