A. Némethi and A. Zaharia have defined the explicit set for a complex polynomial function : and conjectured that the bifurcation set of the global fibration of is given by the union of the set of critical values and the explicit set of . They have proved only the case and is Newton non-degenerate. In the present paper we will prove this for the case , containing the Newton degenerate case, by using toric modifications and give an expression of the bifurcation set of in the words of Newton polygons.
"The bifurcation set of a complex polynomial function of two variables and the Newton polygons of singularities at infinity." J. Math. Soc. Japan 54 (1) 161 - 196, January, 2002. https://doi.org/10.2969/jmsj/1191593959