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A new family of symplectic singularities

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If you have a question about this talk, please contact Gareth Tracey.

Symplectic singularities were defined by Beauville more than 20 years ago. The main classes of known examples are symplectic quotient singularities ℂ2n/Γ (where Γ is a finite subgroup of the symplectic group) and (normalisations of) nilpotent orbit closures. Until very recently, it was suspected that these exhausted all possible isolated symplectic singularities.

In this talk, I will explain three markedly different constructions of a completely new family of isolated symplectic singularities χn (n ≥ 5): as partial resolutions of quotient singularities for the dihedral group of order 2n; as deformations arising via the corresponding Calogero-Moser space; in the universal cover of the nilpotent cone of gln. The special case n=5 had earlier appeared in relation to a particular Slodowy slice in type E8.

This talk is part of the Algebra Seminar series.

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