A new family of isolated symplectic singularities with trivial local fundamental group

Bellamy, G. , Bonnafé, C., Fu, B., Juteau, D., Levy, P. and Sommers, E. (2023) A new family of isolated symplectic singularities with trivial local fundamental group. Proceedings of the London Mathematical Society, (doi: 10.1112/plms.12513) (Early Online Publication)

Abstract

We construct a new infinite family of four-dimensional isolated symplectic singularities with trivial local fundamental group, answering a question of Beauville raised in 2000. Three constructions are presented for this family: (1) as singularities in blowups of the quotient of by the dihedral group of order , (2) as singular points of Calogero–Moser spaces associated with dihedral groups of order at equal parameters, and (3) as singularities of a certain Slodowy slice in the -fold cover of the nilpotent cone in .

• Item Type: Articles
• Additional Information: C. B. is partially supported by the ANR projects GeRepMod (ANR-16-CE40-0010-01) and CATORE (ANR-18-CE40-0024-02). B. F. is supported by the NSFC grant No. 11688101. D. J. is grateful for the support of the ANR project GeRepMod (ANR-16-CE40-0010-01) and of the Charles Simonyi Endowment at the Institute for Advanced Study.
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellamy, Professor Gwyn
• Authors: Bellamy, G., Bonnafé, C., Fu, B., Juteau, D., Levy, P., and Sommers, E.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the London Mathematical Society
• Publisher: London Mathematical Society
• ISSN: 0024-6115
• ISSN (Online): 1460-244X
• Published Online: 23 January 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Proceedings of the London Mathematical Society 2023
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

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