Asymptotic critical value set and Newton polyhedron

2019/11/18 by Susumu Tanabé, Tanabé, Susumu, Gunduz, Abuzer
Computer Science · Mathematics · #14Q20 #32S05 #58K05 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics #Computer science #Construct (python library) #FOS: Mathematics #Face (sociological concept) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Parametric statistics #Polyhedron #Polynomial #Polynomial and algebraic computation #Representation (politics) #Set (abstract data type) #Value (mathematics)

paper · pdf · doi:10.48550/arxiv.1911.07952

openalex publication_date 2019/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an effective method to investigate the asymptotic critical value set of a polynomial map. For this purpose we propose a method to construct rational curves with reduced number of terms present in its parametric representation. In this way we show that the asymptotic critical value set contains the critical value of an polynomial associated to so called bad face of the Newton polyhedron. Our main technical tool is the toric geometry that has been introduced into this question by A.Némethi and A.Zaharia

Related

• The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity
• A short survey on Newton polytopes, tropical geometry and ring of conditions of algebraic torus
• The bifurcation set of a rational function via Newton polytopes
• On the computation of asymptotic critical values of polynomial maps and applications
• Computer Generated Images for Quadratic Rational Maps with a Periodic Critical Point