  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.
