%0 Journal Article
%T The tropical discriminant in positive characteristic
%A Luis Felipe Tabera
%J Mathematics
%D 2014
%I arXiv
%X We study singularities in tropical hypersurfaces defined by a valuation over a field of positive characteristic. We provide a method to compute the set of singular points of a tropical hypersurface in positive characteristic and the p-adic case. This computation is applied to determine all maximal cones of the tropical linear space of univariate polynomials of degree $n$ and characteristic $p$ with a fixed double root and the fan of all tropical polynomials that have $0$ as a double root independently of the characteristic. We also compute, by pure tropical means, the number of vertices, edges and 2-faces of the Newton polytope of the discriminant of polynomials of degree $p$ in characteristic $p$.
%U http://arxiv.org/abs/1403.1051v1