Classification of Enriques surfaces with finite automorphism group in characteristic 2

TL;DR

This paper classifies Enriques surfaces with finite automorphism groups in characteristic 2, detailing their dual graphs and providing explicit examples, completing the classification across all characteristics.

Contribution

It provides a complete classification of Enriques surfaces with finite automorphism groups in characteristic 2, including explicit examples and their canonical coverings.

Findings

Classified supersingular and classical Enriques surfaces into 8 types

Provided explicit examples and dual graph descriptions

Confirmed the classification is complete across all characteristics

Abstract

We classify supersingular and classical Enriques surfaces with finite automorphism group in characteristic 2 into 8 types according to their dual graphs of all $(-2)$-curves (nonsigular rational curves). We give examples of these Enriques surfaces together with their canonical coverings. It follows that the classification of all Enriques surfaces with finite automorphism group in any characteristics has been finished.