  Attached to a vertex algebra $\mathcal{V}$ are two geometric objects. The
associated scheme of $\mathcal{V}$ is the spectrum of Zhu's Poisson algebra
$R_{\mathcal{V}}$. The singular support of $\mathcal{V}$ is the spectrum of the
associated graded algebra $\text{gr}(\mathcal{V})$ with respect to Li's
canonical decreasing filtration. There is a closed embedding from the singular
support to the arc space of the associated scheme, which is an isomorphism in
many interesting cases. In this note we give an example of a non-quasi-lisse
vertex algebra whose associated scheme is reduced, for which the isomorphism is
not true as schemes but true as varieties.
