  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-discriminant, which is the tropicalization of the dual variety
of the projective toric variety given by an integer matrix A, is shown to
coincide with the Minkowski sum of the row space of A and of the
tropicalization of the kernel of A. This leads to an explicit positive formula
for the extreme monomials of any A-discriminant, without any smoothness
assumption.
