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

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 C4$\mathbb {C}^4$ by the dihedral group of order 2d$2d$ , (2) as singular points of Calogero–Moser spaces associated with dihedral groups of order 2d$2d$ at equal parameters, and (3) as singularities of a certain Slodowy slice in the d$d$ ‐fold cover of the nilpotent cone in sld${\mathfrak {s}}{\mathfrak {l}}_d$ .