Tropical tangents for complete intersection curves.

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. [ABSTRACT FROM AUTHOR]