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- W3105839337 abstract "Let $Gamma$ be a finite subgroup of $mathrm{Sp}(V)$. In this article we count the number of symplectic resolutions admitted by the quotient singularity $V / Gamma$. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero-Moser space. In this way, we give a simple formula for the number of $mathbb{Q}$-factorial terminalizations admitted by the symplectic quotient singularity in terms of the dimension of a certain Orlik-Solomon algebra naturally associated to the Calogero-Moser deformation. This dimension is explicitly calculated for all groups $Gamma$ for which it is known that $V / Gamma$ admits a symplectic resolution. As a consequence of our results, we confirm a conjecture of Ginzburg and Kaledin." @default.
- W3105839337 created "2020-11-23" @default.
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- W3105839337 date "2015-09-24" @default.
- W3105839337 modified "2023-09-28" @default.
- W3105839337 title "Counting resolutions of symplectic quotient singularities" @default.
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- W3105839337 doi "https://doi.org/10.1112/s0010437x15007630" @default.
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