Fibrations associated with a pencil of plane curves
type: Item
instance of: scholarly article
title: Fibrations associated with a pencil of plane curves
zbMATH Open document ID: 1030.32023
author: Hélène Maugendre
author: Françoise Michel
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2003-07-06T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73566
review text: Let \(f\) and \(g\) be two holomorphic function germs at the origin \(\mathbb C^2.\) The authors determine the set of atypical values of the pencil \(f_a=f+a g^n\colon (\mathbb C^2, o) \to \mathbb C\), where \(a\in \mathbb C\) and \(n \in \mathbb N^\ast.\) In fact, \(B\subset \mathbb C\) is finite and the pencil is equisingular over \(\mathbb C\setminus B.\) Then they compute irregular values at infinity of polynomial maps \(\mathbb C^2\to\mathbb C,\) study the Milnor fibration of all members of the pencil, and the characteristic polynomials in the pencil. In conclusion, in the case when \(g\) is a coordinate function, it is described the topology of the generic member of the pencil in terms of the minimal resolution of \(f\cdot g.\)
Mathematics Subject Classification ID: 32S55
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 32S15
zbMATH DE Number: 1911466
zbMATH Keywords: polynomial map
zbMATH Keywords: pencil
zbMATH Keywords: atypical value
zbMATH Keywords: irregular value at infinity
zbMATH Keywords: equisingularity
zbMATH Keywords: Milnor fibration
zbMATH Keywords: Euler numbers
zbMATH Keywords: characteristic polynomial
zbMATH Keywords: minimal resolution
reviewed by: Aleksandr G. Aleksandrov
MaRDI profile type: Publication
OpenAlex ID: W2334543853
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DOI: 10.5802/AFST.1011
description: scientific article; zbMATH DE number 1911466