Dominance conjecture for associated varieties of finite vertex-algebra extensions

Let $W$ be a vertex algebra that is a finite extension of a vertex algebra $L$, and let $X_W$ and $X_L$ denote their associated Poisson varieties. Dominance conjecture. The morphism of Poisson algebraic varieties

$$X_W\longrightarrow X_L$$

should be dominant. This conjecture concerns how associated varieties behave under finite extensions and is cited by the source as a conjecture of Arakawa, Etingof, and Moreau.