Surface fibrations with large equivariant automorphism group

TL;DR

This paper classifies surface fibrations with fiber genus at least one that have an infinite equivariant automorphism group, providing insights into their structure over any algebraically closed field.

Contribution

It offers a comprehensive classification of surface fibrations with infinite equivariant automorphism groups, extending understanding across arbitrary algebraically closed fields.

Findings

Classification of fibrations with infinite automorphism groups

Results valid over any algebraically closed field

Insights into automorphism group structures

Abstract

For a relatively minimal surface fibration $f: X\to C$, the equivariant automorphism group of $f$ is, roughly speaking, the group of automorphisms of $X$ preserving the fibration structure. We present a classification of such fibrations of fibre genus $g\ge 1$ with smooth generic fibre over an arbitrary algebraically closed field $\mathbf{k}$ whose equivariant automorphism group is infinite.