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arXiv · 1504.07463

Cox rings of some symplectic resolutions of quotient singularities

Maria Donten-Bury·Maksymilian Grab
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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.

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Maria Donten-Bury, Maksymilian Grab. 2015-04-28. Cox rings of some symplectic resolutions of quotient singularities. https://arxiv.org/abs/1504.07463

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