On the topology of the Newton boundary at infinity
type: Item
instance of: scholarly article
title: On the topology of the Newton boundary at infinity
zbMATH Open document ID: 1159.32016
published in: Journal of the Mathematical Society of Japan
publication date: 2009-01-30T00:00:00Z
review text: 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.
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 32S20
Mathematics Subject Classification ID: 32S40
zbMATH DE Number: 5500751
zbMATH Keywords: global monodromy fibration
zbMATH Keywords: family of polynomials
zbMATH Keywords: Newton polyhedron
zbMATH Keywords: non-degeneracy condition
zbMATH Keywords: singularities at infinity
author: Tien Son Pham
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/06041065
OpenAlex ID: W2017004104
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DOI: 10.2969/JMSJ/06041065
description: scientific article; zbMATH DE number 5500751