Automorphism groups of smooth plane curves with many Galois points

TL;DR

This paper determines the automorphism groups of certain smooth plane curves with multiple Galois points, including a special case where the automorphism group surpasses the Hurwitz bound.

Contribution

It classifies automorphism groups of smooth plane curves with multiple Galois points, identifying cases with exceptional automorphism group sizes.

Findings

Automorphism groups of classified curves are explicitly determined.

Identification of a curve with automorphism group exceeding the Hurwitz bound.

Complete classification of automorphism groups for these curves.

Abstract

We settle the automorphism groups of curves appearing in a classification list of smooth plane curves with at least two Galois points. One of them is an ordinary curve whose automorphism group exceeds the Hurwitz bound.