A birational embedding with two Galois points for certain Artin-Schreier curves

TL;DR

This paper demonstrates that certain Artin-Schreier curves can be embedded into the projective plane with two Galois points, revealing new geometric properties of these curves and their automorphism groups.

Contribution

It establishes the existence of birational embeddings with two Galois points for specific Artin-Schreier curves and those with large automorphism groups.

Findings

Artin-Schreier curves admit such embeddings

Curves with large automorphism groups also have these embeddings

Enhances understanding of the geometric structure of these curves

Abstract

We show that two curves of Artin-Schreier type have a birational embedding into a projective plane with two Galois points. As a consequence, all curves with large automorphism groups in the classification list by Henn have a birational embedding with two Galois points.