# Algebraic curves admitting non-collinear Galois points

## TL;DR

This paper establishes criteria for algebraic curves to have embeddings with non-collinear Galois points, provides a new example of such curves, and characterizes Fermat curves through this property.

## Contribution

It introduces a new criterion for the existence of non-collinear Galois points and offers a novel characterization of Fermat curves based on these points.

## Key findings

- Presented a criterion for birational embeddings with non-collinear Galois points.
- Constructed a new example of a plane curve with non-collinear Galois points.
- Characterized Fermat curves using non-collinear Galois points.

## Abstract

A criterion for the existence of a birational embedding into a projective plane with non-collinear Galois points for algebraic curves is presented. A new example of a plane curve with non-collinear Galois points as an application is described. Furthermore, a new characterization of the Fermat curve in terms of non-collinear Galois points is presented.