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arXiv · 2112.15494

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

Gwyn Bellamy·Cédric Bonnafé·Baohua Fu·Daniel Juteau·Paul Levy·Eric Sommers
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Abstract

We construct a new infinite family of 4-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 $\mathbb{C}^4$ by the dihedral group of order $2d$, (2) as singular points of Calogero-Moser spaces associated with dihedral groups of order $2d$ at equal parameters, (3) as singularities of a certain Slodowy slice in the $d$-fold cover of the nilpotent cone in ${\mathfrak{sl}}_d$.

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Gwyn Bellamy, Cédric Bonnafé, Baohua Fu, Daniel Juteau, Paul Levy, Eric Sommers. 2021-12-23. A new family of isolated symplectic singularities with trivial local fundamental group. https://arxiv.org/abs/2112.15494

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