Cox rings of some symplectic resolutions of quotient singularities

Abstract

We investigate Cox rings of symplectic resolutions of quotients of ${\mathbb{C}}^{2n}$ by finite symplectic group actions. We propose a finite generating set of the Cox ring of a symplectic resolution and prove that under a condition concerning monomial valuations it is sufficient. Also, three 4-dimensional examples are described in detail. Generators of the (expected) Cox rings of symplectic resolutions are computed and in one case a resolution is constructed as a GIT quotient of the spectrum of the Cox ring.

27 pages

References in corpus (1)

• On singular Calogero-Moser spaces

Cited by in corpus (2)

• Cox rings and symplectic quotient singularities with torus action
• Crepant resolutions of 3-dimensional quotient singularities via Cox rings