On the (non)existence of symplectic resolutions for imprimitive symplectic reflection groups

Abstract

We study the existence of symplectic resolutions of quotient singularities V/G where V is a symplectic vector space and G acts symplectically. Namely, we classify the symplectically irreducible and imprimitive groups, excluding those of the form $K⋊S_2$ where $K < \SL_2(\C)$, for which the corresponding quotient singularity admits a projective symplectic resolution. As a consequence, for $\dim V\ne 4$, we classify all quotient singularities $V/G$ admitting a projective symplectic resolution which do not decompose as a product of smaller-dimensional quotient singularities, except for at most four explicit singularities, that occur in dimensions at most 10, for whom the question of existence remains open.

21 pages

References in corpus (3)

• McKay equivalence for symplectic resolutions of singularities
• On singular Calogero-Moser spaces
• A symplectic resolution for the binary tetrahedral group

Cited by in corpus (1)

• Poisson traces, D-modules, and symplectic resolutions