# Algebraic curves admitting the same Galois closure for two projections

## TL;DR

This paper establishes a criterion for when an algebraic curve admits a plane model with identical Galois closures from two points, and applies it to show the Hermitian curve's unique property in positive characteristic.

## Contribution

It introduces a new criterion for the existence of a plane model with equal Galois closures from two points and applies it to characterize the Hermitian curve in positive characteristic.

## Key findings

- The criterion determines when a plane model of a curve has identical Galois closures from two points.
- The Hermitian curve in positive characteristic is characterized as the Galois closure of projections from two non-uniform points.
- The result links algebraic curve models with Galois closure properties in positive characteristic.

## Abstract

A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it is proved that the Hermitian curve in positive characteristic coincides with the Galois closures of projections of some plane curve from some two non-uniform points.