# Finite groups acting on elliptic surfaces

## TL;DR

This paper investigates the structure and properties of finite automorphism groups acting on elliptic surfaces, revealing unbounded subgroups in certain cases and analyzing fiber and base actions.

## Contribution

It provides new insights into the automorphism groups of elliptic surfaces, including unbounded subgroups and their actions on fibers and bases.

## Key findings

- Automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups.
- Finite groups can act along fibers and bases of elliptic fibrations on various surfaces.
- Observations on the structure of automorphism groups in different elliptic surface contexts.

## Abstract

We show that automorphism groups of Hopf and Kodaira surfaces have unbounded finite subgroups. For elliptic fibrations on Hopf, Kodaira, bielliptic, and K3 surfaces, we make some observations on finite groups acting along the fibers and on the base of such a fibration.