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- W2962689857 abstract "Let X ⊂ ℂ3 be a surface with an isolated singularity at the origin, given by the equation Q(x, y, z) = 0, where Q is a weighted-homogeneous polynomial. In particular, this includes the Kleinian surfaces X = ℂ2/G for G < SL2(ℂ) finite. Let Y ≔ SnX be the n-th symmetric power of X. We compute the zeroth Poisson homology HP0(𝒪Y), as a graded vector space with respect to the weight grading, where 𝒪Y is the ring of polynomial functions on Y. In the Kleinian case, this confirms a conjecture of Alev, that , where Weyl2n is the Weyl algebra on 2n generators. That is, the Brylinski spectral sequence degenerates in degree zero in this case. In the elliptic case, this yields the zeroth Hochschild homology of symmetric powers of the elliptic algebras with three generators modulo their center, Aγ, for all but countably many parameters γ in the elliptic curve. As a consequence, we deduce a bound on the number of irreducible finite-dimensional representations of all quantizations of Y. This includes the noncommutative spherical symplectic reflection algebras associated to Gn ⋊ Sn." @default.
- W2962689857 created "2019-07-30" @default.
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- W2962689857 date "2012-01-01" @default.
- W2962689857 modified "2023-10-11" @default.
- W2962689857 title "Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities" @default.
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- W2962689857 doi "https://doi.org/10.1515/crelle.2011.124" @default.
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