Non-degenerate mixed functions

Abstract

Mixed functions are analytic functions in variables z₁, ..., z_n and their conjugates $¥bar z_1$, ..., $¥bar z_n$. We introduce the notion of Newton non-degeneracy for mixed functions and develop a basic tool for the study of mixed hypersurface singularities. We show the existence of a canonical resolution of the singularity, and the existence of the Milnor fibration under the strong non-degeneracy condition.