Milnor fibration at infinity for mixed polynomials

TL;DR

This paper investigates the conditions under which mixed polynomials admit Milnor fibrations at infinity, extending existing theorems to a broader class of polynomials using non-degeneracy conditions.

Contribution

It establishes a global Milnor fibration theorem for strongly non-degenerate and convenient mixed polynomials, generalizing previous results.

Findings

Proves a Milnor fibration theorem at infinity for mixed polynomials.

Extends Oka's fibration theorem to a broader class of polynomials.

Uses strong non-degeneracy to ensure the existence of fibrations.

Abstract

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial $f: \bR^{2n} \to \bR^2$. By using strong non-degeneracy condition, we prove a counterpart of N\'emethi and Zaharia's fibration theorem. In particular, we obtain a global version of Oka's fibration theorem for strongly non-degenerate and convenient mixed polynomials.