On the Newton Polytope of the Morse Discriminant

Abstract: A famous classical result by Gelfand, Kapranov and Zelevinsky provides a combinatorial description of the vertices of the Newton polytope of the A-discriminant (the closure of the set of all non-smooth hypersurfaces defined by polynomials with the given support A). Namely, it gives a surjection from the set of all convex triangulations of the convex hull of the set A with vertices in A (or, equivalently, the set of all possible combinatorial types of smooth tropical hypersurfaces defined by tropical polynomials with support A) onto the set of vertices of this Newton polytope. In my talk, I will discuss a similar problem for the Morse discriminant — the closure of the set of all polynomials with the given support A which are non-Morse if viewed as polynomial maps. Namely, for a 1-dimensional support set A, there is a surjection from the set of all possible combinatorial types of so-called Morse tropical polynomials onto the vertices of the Newton polytope of the Morse discriminant.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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