Hypertoric Poisson homology in degree zero

TL;DR

This paper proves a strengthened conjecture about degree zero Poisson homology for hypertoric varieties and proposes an analogous conjecture for Hochschild homology of their quantizations.

Contribution

It strengthens a conjecture on Poisson homology and proves it for hypertoric varieties, also proposing a related conjecture for Hochschild homology.

Findings

Proof of the strengthened conjecture for hypertoric varieties

Formulation of an analogous conjecture for Hochschild homology

Advancement in understanding Poisson and Hochschild homologies in symplectic resolutions

Abstract

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