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

Abstract

Let $\mathcal{X}$ be a projective algebraic curve and denote by ${\mathcal{X}}^{{}^{\prime }}$ its strict dual curve. The map $\gamma :\mathcal{X}⟶{\mathcal{X}}^{{}^{\prime }}$ 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.