Associated scheme and singular support of a vertex algebra


Salle Duhem M3
Andrew Linshaw
Université de Denver
Vendredi, 10 Mai, 2019 - 14:00 - 15:00

I will review the basics of vertex algebra theory, and then discuss two geometric objects that have been attached to any vertex algebra $V$ by T. Arakawa: the associated scheme $X_{V}$, and the singular support $SS(V)$. There is always closed embedding of $SS(V)$ in the arc space of $X_V$. T. Arakawa and A. Moreau have asked when this map is an isomorphism, and if not, whether the induced map on reduced schemes is an isomorphism. I will discuss the case where $V$ is the Zamolodchikov $W_3$ algebra with central charge $c = -2$. In this case, $X_V$ is the cuspidal curve $x^3 = y^2$, and the above map fails to be an isomorphism of schemes, but is an isomorphism of reduced schemes. This a joint work with T. Arakawa, and our result relies on J. Sebag's observation that the arc space of this curve is not reduced.