The tropical discriminant of a polynomial map on the plane

Abstract: The discriminant, $D(f)$, of a map $f:X\to Y$ is the set of images of its critical points. Approximating $D(f)$ presents a fruitful insight for solving numerous problems in mathematics. However, standard methods for achieving this rely on elimination techniques which can be excessively inefficient.

I will present a purely combinatorial procedure for computing the tropical curve in $\mathbb{R}^2$ of the discriminant of a polynomial map on the plane satisfying some mild genericity conditions. Thanks to the advances in tropical geometry in the last 20 years, this new procedure gives rise to a more efficient algorithm for approximating $D(f)$, and for working out its geometrical/topological invariants.

algebraic geometrycombinatorics

Audience: researchers in the topic

(LAGARTOS) Latin American Real and Tropical Geometry Seminar

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