Equivariant Kuznetsov components for cubic fourfolds with a symplectic involution

TL;DR

This paper investigates the equivariant Kuznetsov component of a cubic fourfold with a symplectic involution, establishing its equivalence to the derived category of a K3 surface derived from the fixed locus of the involution.

Contribution

It demonstrates that the equivariant Kuznetsov component is equivalent to the derived category of a K3 surface, linking cubic fourfolds with symplectic involutions to K3 surfaces.

Findings

Equivariant Kuznetsov component is equivalent to a K3 surface derived category.

The K3 surface arises from the fixed locus of the symplectic involution.

Provides a categorical link between cubic fourfolds and K3 surfaces.

Abstract

We study the equivariant Kuznetsov component $\mathrm{Ku}_G(X)$ of a general cubic fourfold $X$ with a symplectic involution. We show that $\mathrm{Ku}_G(X)$ is equivalent to the derived category $D^b(S)$ of a $K3$ surface $S$, where $S$ is given as a component of the fixed locus of the induced symplectic action on the Fano variety of lines on $X$.