Automorphism group schemes of bielliptic and quasi-bielliptic surfaces

TL;DR

This paper determines the automorphism schemes of bielliptic and quasi-bielliptic surfaces over algebraically closed fields, extending previous complex number results and filling gaps in characteristic zero classifications.

Contribution

It generalizes the classification of automorphism schemes of these surfaces to arbitrary characteristic, including previously missing cases.

Findings

Automorphism schemes are fully characterized over algebraically closed fields.

New cases of automorphism groups are identified in positive characteristic.

The work extends and completes existing classifications in characteristic zero.

Abstract

Bielliptic and quasi-bielliptic surfaces form one of the four classes of minimal smooth projective surfaces of Kodaira dimension $0$. In this article, we determine the automorphism schemes of these surfaces over algebraically closed fields of arbitrary characteristic, generalizing work of Bennett and Miranda over the complex numbers; we also find some cases that are missing from the classification of automorphism groups of bielliptic surfaces in characteristic $0$.