Asymptotic critical value set and Newton polyhedron

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.