Journal of the Mathematical Society of Japan

On the fundamental groups of the complements of plane singular sextics

Christophe EYRAL and Mutsuo OKA

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Abstract

Recently, Oka-Pho proved that the fundamental group of the complement of any plane irreducible tame torus sextic is not abelian. We compute here the fundamental groups of the complements of some plane irreducible sextics which are not of torus type. For all our examples, we obtain that the fundamental group is abelian.

Article information

Source
J. Math. Soc. Japan, Volume 57, Number 1 (2005), 37-54.

Dates
First available in Project Euclid: 13 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1160745812

Digital Object Identifier
doi:10.2969/jmsj/1160745812

Mathematical Reviews number (MathSciNet)
MR2114719

Zentralblatt MATH identifier
1070.14031

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]

Keywords
fundamental groups complements of plane singular curves Zariski-van Kampen theorem pencils of lines monodromies

Citation

EYRAL, Christophe; OKA, Mutsuo. On the fundamental groups of the complements of plane singular sextics. J. Math. Soc. Japan 57 (2005), no. 1, 37--54. doi:10.2969/jmsj/1160745812. https://projecteuclid.org/euclid.jmsj/1160745812


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