A birational embedding with two Galois points for quotient curves

TL;DR

This paper provides a criterion for when quotient curves can be embedded birationally with two Galois points, and applies it to construct new examples of plane curves with this property.

Contribution

It introduces a new criterion for the existence of such embeddings and applies it to specific quotient curves, producing novel examples.

Findings

New criterion for birational embedding with two Galois points

Application to cyclic subcovers of Giulietti-Korchmaros and Skabelund curves

Construction of new plane curves with two Galois points

Abstract

A criterion for the existence of a birational embedding with two Galois points for quotient curves is presented. We apply our criterion to several curves, for example, some cyclic subcovers of the Giulietti-Korchmaros curve or of the curves constructed by Skabelund. They are new examples of plane curves with two Galois points.