On the topology of the Newton boundary at infinity

Abstract

We are interested in a global version of Lê-Ramanujam $\mu$ -constant theorem from the Newton polyhedron point of view. More precisely, we prove a stability theorem which says that the global monodromy fibration of a polynomial function with Newton non-degenerate is uniquely determined by its Newton boundary at infinity. Furthermore, the continuity of atypical values for a family of complex polynomial functions also is considered.