Bounds for the order of automorphism groups of cyclic covering fibrations of a ruled surface

TL;DR

This paper investigates upper bounds for the size of automorphism groups in cyclic covering fibrations on ruled surfaces, extending previous work on hyperelliptic fibrations to a broader class.

Contribution

It establishes new bounds for automorphism groups in cyclic covering fibrations, generalizing prior results from hyperelliptic cases.

Findings

Derived upper bounds for automorphism group orders

Extended known results from hyperelliptic to cyclic covering fibrations

Provided theoretical framework for automorphism group analysis

Abstract

We study the order of automorphism groups of cyclic covering fibrations of a ruled surface. Arakawa and later Chen studied it for hyperelliptic fibrations and gave the upper bound. The purpose of present paper is to pursue the analog for cyclic covering fibrations.