Invariance of the global monodromies in families of nondegenerate polynomials in two variables

Abstract

We are interested in a global version of Lê-Ramanujam μ-constant theorem for polynomials. We consider an analytic family {f_s}, s ∈ [0, 1], of complex polynomials in two variables, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber of f_s is constant, then we show that the global monodromy fibrations of f_s are all isomorphic, and that the degree of f_s is constant (up to an algebraic automorphism of C²).