Tropical Discriminants
Algebraic Geometry
2007-05-23 v3 Combinatorics
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-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.
Keywords
Cite
@article{arxiv.math/0510126,
title = {Tropical Discriminants},
author = {Alicia Dickenstein and Eva Maria Feichtner and Bernd Sturmfels},
journal= {arXiv preprint arXiv:math/0510126},
year = {2007}
}
Comments
Major revisions, including several improvements and the correction of Section 5. To appear: Journal of the American Mathematical Society