Dg categories of cubic fourfolds

Abstract

We prove a reconstruction theorem à la Calabrese-Groechenig for the moduli space parametrizing skyscraper sheaves on a smooth projective variety when these are considered as a system of points in the dg category of perfect complexes on the variety, as axiomatized by Toën and Vaquié. This result is then used to show that, for a cubic fourfold $Y\subset {\mathbb{P}}_{\mathbb{C}}^5$, the Kuznetsov category ${\mathcal{A}}_Y$ is geometric (possibly twisted) if and only if a dg enhancement $T_Y$ of ${\mathcal{A}}_Y$ admits a system of points whose associated moduli space is a (possibly twisted) K3 surface.

arXiv comment22 pages, comments welcome

References in corpus (1)

• Hodge theory and derived categories of cubic fourfolds