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.

中文翻译：

---

与 Hypertoric 变异相关的顶点代数

我们构建了一个与辛奇点/分辨率族相关的顶点代数族，称为hypertoric簇。虽然 hypertoric 变体是由与环面作用相关的某个哈密顿归约构造的，但我们的顶点代数是由（半无限）BRST 归约构造的。该构造以代数几何方式进行，我们在局部化顶点代数的超复变体上构造了 $\hbar$-adic 顶点代数的层。我们通过给出明确的共形向量来展示顶点代数何时是顶点算子代数。我们还展示了顶点代数的朱代数，与非负分级顶点代数相关的结合代数，给出了超复变体的坐标环的某个过滤量化系列。