Automorphism groups of rational elliptic and quasi-elliptic surfaces in all characteristics

TL;DR

This paper classifies automorphism groups of rational elliptic and quasi-elliptic surfaces across all characteristics, focusing on those with trivial actions on the Picard group, and applies findings to Enriques surfaces in characteristic 2.

Contribution

It provides a comprehensive classification of automorphism groups of rational elliptic and quasi-elliptic surfaces, including those with trivial Picard group action, extending understanding across all characteristics.

Findings

Classification of surfaces with non-trivial automorphisms acting trivially on Picard group

Identification of automorphism groups for Enriques surfaces in characteristic 2

Extension of automorphism group analysis to all characteristics

Abstract

We study the groups of automorphisms of rational algebraic surfaces that admit a relatively minimal pencil of curves of arithmetic genus one over an algebraically closed field of arbitrary characteristic. In particular, we classify such surfaces that admit non-trivial automorphisms that act trivially on the Picard group. As an application, we classify classical Enriques surfaces in characteristic $2$ that admit non-trivial numerically trivial automorphisms.