Tropical Discriminants

Details Tropical Discriminants Tropical Discriminants

2005-10-06

arxiv.org/abs/math/0510126v3

Mathematics

Algebraic Geometry

Major revisions, including several improvements and the correction of Section 5. To appear: Journal of the American Mathematic

Scientific paper

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.

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