Attached to a vertex algebra V are two geometric objects. The associated scheme of V is the spectrum of Zhu’s Poisson algebra RV. The singular support of V is the spectrum of the associated graded algebra gr (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.
CITATION STYLE
Arakawa, T., & Linshaw, A. R. (2019). Singular Support of a Vertex Algebra and the Arc Space of Its Associated Scheme. In Progress in Mathematics (Vol. 330, pp. 1–17). Springer Basel. https://doi.org/10.1007/978-3-030-23531-4_1
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