In the fist part of my talk, I will present basics on vertex algebra and arc spaces, which provide interesting examples of commutative vertex algebras and vertex Poisson algebras (when the corresponding variety is Poisson). In the second part, I will introduce the notion of chiral symplectic cores which can be viewed as chiral analogs of symplectic leaves. As an application I will 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 arc space of its associated variety. If times, I will also present an application to the vertex Poisson center of the coordinate ring of the arc space of Slodowy slices. This is based on a joint work with Tomoyuki Arakawa