Tropical Discriminants

By Alicia Dickenstein, Eva Maria Feichtner, Bernd Sturmfels. 2005

135 citations recorded by the source corpus.

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.

View Paper: https://www.semanticscholar.org/paper/3c0a499509709548871609285394dd4cab6a002f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Eric Katz
2. Bernd Sturmfels
3. Jenia Tevelev
4. Yutaka Matsui
5. K. Takeuchi
6. Sam Payne
7. June Huh
8. Walter Gubler

Citations in the corpus

• A Tropical Toolkit (2006, background): “=1 mσ jl (−h(vj)). By varying h, we see that we have the balancing condition at τ. 8. Deformations of Subschemes into Torus Orbits This section is a generalization of the results of second section of [7]. Let Y be a smooth toric scheme defined over k and X⊆ Y, a purely k-dimensional closed subscheme.”
• A geometric degree formula for A-discriminants and Euler obstructions of toric varieties (2008, methodology): “(3.31) Note that if the dual defect of XA is zero the degree formula of X ∗ A for singular XA’s was also obtained by Dickenstein-Feichtner-Sturmfels [5].”
• ELIMINATION THEORY FOR TROPICAL VARIETIES (2007, background): “7) agrees with the formulation in the Introduction (and in [6, 20]):”