Arc spaces and chiral symplectic cores

Abstract

We introduce the notion of chiral symplectic cores in a vertex Poisson variety, which can be viewed as analogs of symplectic leaves in Poisson varieties. As an application we show that any quasi-lisse vertex algebra is a quantization of the arc space of its associated variety, in the sense that its reduced singular support coincides with the reduced arc space of its associated variety. We also show that the coordinate ring of the arc space of Slodowy slices is free over its vertex Poisson center, and the latter coincides with the vertex Poisson center of the coordinate ring of the arc space of the dual of the corresponding simple Lie algebra.

arXiv commentA number of mistakes corrected. This version will appear in Publications of the RIMS, special issue dedicated to Masaki Kashiwara

References in corpus (7)

• Infinite Chiral Symmetry in Four Dimensions
• Jet Schemes of Locally Complete Intersection Canonical Singularities
• Vertex operator algebras, Higgs branches, and modular differential equations
• VOAs labelled by complex reflection groups and 4d SCFTs
• Joseph ideals and lisse minimal W-algebras
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Cited by in corpus (6)

• Trialities of $\mathcal{W}$-algebras
• Singular support of a vertex algebra and the arc space of its associated scheme
• Some remarks on associated varieties of vertex operator superalgebras
• Standard monomials and invariant theory for arc spaces III: special linear group
• Derived gluing construction of chiral algebras
• Vertex Algebras and Commutative Algebras