Tropical discriminants

Abstract

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