On the Newton Polytope of the Morse Discriminant

Arina Voorhaar (Geneva)

13-Jan-2022, 13:00-14:00 (2 years ago)

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.

algebraic geometrycombinatorics

Audience: researchers in the topic


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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