The quasi-lisse conjecture for the vertex algebras $\mathcal{C}_p$

Let $\mathcal{C}_p$ be the vertex operator algebra considered in the paper. A vertex operator algebra is quasi-lisse when its associated variety has finitely many symplectic leaves. Quasi-lisse conjecture. The vertex operator algebra $\mathcal{C}_p$ is quasi-lisse for all $p$. The expectation is based on the cases $p=2,3,4,5$, previous computations, and the modularity theorem stated in the surrounding text; the supplied passage does not give a proof for all $p$.