Algebraic curves with collinear Galois points

TL;DR

This paper establishes a criterion for when algebraic curves can be embedded into a projective plane with three collinear Galois points and explores the conditions under which automorphisms extend to linear transformations.

Contribution

It provides a new criterion for the existence of certain embeddings of algebraic curves with collinear Galois points and discusses automorphism extendability.

Findings

A criterion for birational embedding with three collinear Galois points.

Conditions under which automorphisms extend to linear transformations.

Insights into the structure of algebraic curves with Galois points.

Abstract

A criterion for the existence of a birational embedding into a projective plane with three collinear Galois points for algebraic curves is presented. The extendability of an automorphism induced by a Galois point to a linear transformation of the projective plane is also discussed, under the assumption that two Galois points exist.