# Separable degree of the Gauss map and strict dual curves over finite fields

## TL;DR

This paper investigates the separable degree of the Gauss map for algebraic curves over finite fields, generalizing known results and characterizing specific types of strange curves.

## Contribution

It extends the understanding of the Gauss map's separable degree to broader classes of curves over finite fields and characterizes certain plane strange curves.

## Key findings

- Generalized the separable degree of the Gauss map for finite field curves.
- Provided a characterization of specific plane strange curves.
- Extended known results on Frobenius nonclassical curves.

## Abstract

Let $\mathcal{X}$ be a projective algebraic curve and denote by $\mathcal{X}^{'}$ its strict dual curve. The map $\gamma:\mathcal{X} \longrightarrow \mathcal{X}^{'}$ is called (strict) Gauss map of $\mathcal{X}$. In this manuscript, we study the separable degree of the Gauss map of curves defined over finite fields. In particular, we give a generalization of a known result on the separable degree of the Gauss map of plane Frobenius nonclassical curves. We also obtain a characterization of certain plane strange curves.