Bounds for the order of automorphism groups of cyclic covering fibrations of an elliptic surface

TL;DR

This paper investigates bounds on the size of automorphism groups of cyclic covering fibrations of elliptic surfaces, relating group order to geometric invariants like genus and canonical divisor.

Contribution

It provides new estimates for automorphism group sizes based on geometric invariants of cyclic covering fibrations of elliptic surfaces.

Findings

Derived bounds for automorphism group orders

Expressed bounds in terms of genus and covering degree

Linked automorphism group size to canonical divisor square

Abstract

We study automorphism groups of fibered surfaces for finite cyclic covering fibrations of an elliptic surface. We estimate the order of a finite subgroup of automorphism groups in terms of the genus of the fiber, the genus of the base curve, the covering degree and the square of the relative canonical divisor.