Milnor fibration and fibred links at infinity

TL;DR

This paper establishes a criterion for when the multi-link at infinity of a polynomial's zero fiber is fibred, based on the regularity of values at infinity, linking algebraic properties to topological fibering.

Contribution

It provides a necessary and sufficient condition for the multi-link at infinity to be fibred, connecting the concept of regular values at infinity with fibred multi-links in complex polynomial maps.

Findings

Multi-link at infinity is fibred iff all non-zero values are regular at infinity.

The paper characterizes fibred multi-links in terms of regularity at infinity.

Provides a topological criterion linking algebraic regularity to fibering properties.

Abstract

For a polynomial $f$ in two complex variables, we prove that the multi-link at infinity of the 0-fiber $f^{-1}(0)$ is a fibred multi-link if and only if all the values different from 0 are regular at infinity.