Separable Degree of the Gauss Map and Strict Dual Curves Over Finite Fields

Abstract

Let $$\mathcal X$$ be a non-degenerate 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.