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 $X^{\ast }$ and tangential variety $\tau (X)$ of $X$. In particular, we are able to compute the degrees of $X^{\ast }$ and $\tau (X)$ and the Newton polytope of $\tau (X)$ without using any elimination theory.

arXiv comment49 pages, 6 figures, 9 tables