The Newton Polytope of the Morse Discriminant of a Univariate Polynomial

Abstract

In this paper we compute the Newton polytope ${\mathcal{M}}_A$ of the Morse discriminant in the space of univariate polynomials with the given support set $A.$ Namely, we establish a surjection between the set of all combinatorial types of Morse univariate tropical polynomials and the vertices of ${\mathcal{M}}_A.$

29 pages, 11 figures; corrected typos