A Refined Derived Torelli Theorem for Enriques surfaces, II: the non-generic case

TL;DR

This paper proves that in non-generic cases over algebraically closed fields with characteristic not 2, Enriques surfaces are uniquely determined by their Kuznetsov components, extending previous generic case results.

Contribution

It extends the derived Torelli theorem for Enriques surfaces to non-generic cases, completing the classification in this setting.

Findings

Enriques surfaces are isomorphic if their Kuznetsov components are equivalent in non-generic cases.

The result applies over algebraically closed fields with characteristic not 2.

Completes the derived Torelli theorem for all Enriques surfaces.

Abstract

We prove that two Enriques surfaces defined over an algebraically closed field of characteristic different from $2$ are isomorphic if their Kuznetsov components are equivalent. This improves and completes our previous result joint with Nuer where the same statement is proved for generic Enriques surfaces.