The derived category of a non generic cubic fourfold containing a plane

TL;DR

This paper establishes a connection between the derived category of a resolution of a specific algebraic variety associated with a non generic cubic fourfold containing a plane and the Kuznetsov component of the fourfold's derived category, revealing new categorical equivalences.

Contribution

It introduces an Azumaya algebra on the resolution of a singular double cover linked to the fourfold and proves an equivalence of derived categories involving this algebra and the Kuznetsov component.

Findings

Derived category of the resolution twisted by Azumaya algebra is equivalent to Kuznetsov component.

Constructs an Azumaya algebra on the resolution of singularities of a related double cover.

Provides a categorical description for non generic cubic fourfolds containing a plane.

Abstract

We describe an Azumaya algebra on the resolution of singularities of the double cover of a plane ramified along a nodal sextic associated to a non generic cubic fourfold containing a plane. We show that the derived category of such a resolution, twisted by the Azumaya algebra, is equivalent to the Kuznetsov component in the semiorthogonal decomposition of the derived category of the cubic fourfold.