Title: Vertex algebras associated with hypertoric varieties,
Abstract: We construct a family of vertex algebras associated with a family of
symplectic singularity/resolution, called hypertoric varieties. While the
hypertoric varieties are constructed by a certain Hamiltonian reduction
associated with a torus action, our vertex algebras are constructed by
(semi-infinite) BRST reduction. The construction works algebro-geometrically
and we construct sheaves of $\hbar$-adic vertex algebras over hypertoric
varieties which localize the vertex algebras. We show when the vertex algebras
are vertex operator algebras by giving explicit conformal vectors. We also show
that the Zhu algebras of the vertex algebras, associative algebras associated
with non-negatively graded vertex algebras, gives a certain family of filtered
quantizations of the coordinate rings of the hypertoric varieties.