On the topology of the Newton boundary at infinity
The author studies the monodromy fibration of a complex polynomial function \( f:\mathbb{C}^{n}\to \mathbb{C}\) at infinity i.e. the fibration \[ f:f^{-1}(S_{r})\to S_{r} \] where \(S_{r}=\{z\in \mathbb{C}:| z| =r\}\) is a circle of sufficiently large radius \(r\gg 0\) (it means that the disc \(\{z\in \mathbb{C} :| z| <r\}\) contains the all critical values of \(f\) and the all critical values of \(f\) at infinity). He proves that if \(f\) and \(g\) have the same Newton boundary at infinity and they are non-degenerate at infinity (these notions are defined similarly as in the local case) then \(f\) and \(g\) have isomorphic monodromy fibrations at infinity.
scientific article; zbMATH DE number 5500751
scientific article