Rights statement: This is the peer reviewed version of the following article: 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. Proc. London Math. Soc., 126: 1496-1521. https://doi.org/10.1112/plms.12513 which has been published in final form at https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12513 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.
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Final published version
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| <mark>Journal publication date</mark> | 31/05/2023 |
|---|---|
| <mark>Journal</mark> | Proceedings of the London Mathematical Society |
| Issue number | 5 |
| Volume | 126 |
| Number of pages | 26 |
| Pages (from-to) | 1496-1521 |
| Publication Status | Published |
| Early online date | 26/01/23 |
| <mark>Original language</mark> | English |
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 (Formula presented.) by the dihedral group of order (Formula presented.), (2) as singular points of Calogero–Moser spaces associated with dihedral groups of order (Formula presented.) at equal parameters, and (3) as singularities of a certain Slodowy slice in the (Formula presented.) -fold cover of the nilpotent cone in (Formula presented.).