Tropical tangents for complete intersection curves

Abstract:

We consider the tropicalization of tangent lines to a complete intersection curve $X$ in $\mathbb {P}^n$. Under mild hypotheses, we describe a procedure for computing the tropicalization of the image of the Gauss map of $X$ in terms of the tropicalizations of the hypersurfaces cutting out $X$. We apply this to obtain descriptions of the tropicalization of the dual variety $X^*$ and tangential variety $\tau (X)$ of $X$. In particular, we are able to compute the degrees of $X^*$ and $\tau (X)$ and the Newton polytope of $\tau (X)$ without using any elimination theory.