Non-degenerate mixed functions

TL;DR

This paper introduces a new concept of Newton non-degeneracy for mixed functions, providing tools for analyzing their singularities, including a canonical resolution and conditions for the Milnor fibration.

Contribution

It defines Newton non-degeneracy for mixed functions and establishes foundational results like canonical resolution and Milnor fibration existence under this condition.

Findings

Defined Newton non-degeneracy for mixed functions

Established a canonical resolution of singularities

Proved Milnor fibration exists under strong non-degeneracy

Abstract

Mixed functions are analytic functions in variables $z_1,..., z_n$ 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.