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Etingof and Schedler formulated a conjecture about the degree zero Poissonhomology of an affine cone that admits a projective symplectic resolution. Westrengthen this conjecture in general and prove the strengthened version forhypertoric varieties. We also formulate an analogous conjecture for the degreezero Hochschild homology of a quantization of such a variety.

Hypertoric Poisson homology in degree zero