  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.N\'emethi and A.Zaharia
