Tropical discriminants

Abstract

Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gelfand, Kapranov and Zelevinsky. The tropical A-discriminant is the tropicalization of the dual variety of the projective toric variety given by an integer matrix A. This tropical algebraic variety is shown to coincide with the Minkowski sum of the row space of A and the tropicalization of the kernel of A. This leads to an explicit positive formula for all the extreme monomials of any A-discriminant.