Invariance of the global monodromies in families of nondegenerate polynomials in two variables (Q988523)

The author is interested in a global version of the Lê-Ramanujam \(\mu \)-constant theorem for polynomials. He considers an analytic family \(\{f_s\}\), \(s \in [0, 1]\), of complex polynomials in two variables that are Newton non-degenerate. By assuming that the Euler characteristic of a generic fiber of \(f_s\) is constant, he then shows that the global monodromy fibrations of \(f_s\) are all isomorphic, and that the degree of \(f_s\) is constant (up to an algebraic C\(^{2}\)-automorphism).