On the Fano dimension of an Enriques surface

TL;DR

This paper constructs specific Fano fourfolds that contain the derived category of a general Enriques surface, reducing the known Fano dimension from six to four.

Contribution

It improves previous results by explicitly constructing Fano fourfolds with the Enriques surface's derived category as a component, lowering the Fano dimension.

Findings

Fano dimension of a general Enriques surface is lowered from six to four.

Constructs a family of Fano fourfolds with desired derived category properties.

Advances understanding of the relationship between Fano varieties and Enriques surfaces.

Abstract

We construct a family of Fano fourfolds with the derived category of coherent sheaves of a general Enriques surface as semiorthogonal component. This improves a result of Kuznetsov, lowering the Fano dimension of a general Enriques surface from six to four.