On facets of the Newton polytope for the discriminant of the polynomial system

TL;DR

This paper investigates the geometric structure of the Newton polytope associated with the discriminant of Laurent polynomial systems, employing tropical geometry and combinatorial methods to analyze its facets.

Contribution

It introduces a tropical approach combined with a combinatorial construction to study the facets of the Newton polytope for polynomial discriminants.

Findings

Characterization of normal directions to facets

Application of tropical geometry techniques

Extension of combinatorial methods to discriminant polytopes

Abstract

We study normal directions to facets of the Newton polytope of the discriminant of the Laurent polynomial system via the tropical approach. We use the combinatorial construction proposed by Dickenstein, Feichtner and Sturmfels for the tropicalization of algebraic varieties admitting a parametrization by a linear map followed by a monomial map.