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VOL. 56 | 2009 Topology of abelian pencils of curves
Mutsuo Oka

Editor(s) Jean-Paul Brasselet, Shihoko Ishii, Tatsuo Suwa, Michel Vaquie

Abstract

We study the geometry of a linear system of plane curves $C(\tau) (\tau \in \mathbb{C})$ spanned by two irreducible curves $C$, $C'$ of degree $d$ such that $\pi_1 (\mathbb{P}^2 - C \cup C')$ is abelian. We will show that the fundamental group $\pi_1 (\mathbb{C}^2 - C(\vec{\tau}))$ is isomorphic to $\mathbb{Z} \times F(r- 1)$ for a generic $\vec{\tau}$ where $\vec{\tau} = (\tau_1, \dots, \tau_r)$ and $C(\vec{\tau}) = C(\tau_1) \cup \dots \cup C(\tau_r)$.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1201.14022
MathSciNet: MR2604085

Digital Object Identifier: 10.2969/aspm/05610225

Subjects:
Primary: 14H30, 14H45

Rights: Copyright © 2009 Mathematical Society of Japan

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