Advanced Studies in Pure Mathematics

On irreducible sextics with non-abelian fundamental group

Alex Degtyarev

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Abstract

We calculate the fundamental groups $\pi = \pi_1 (\mathbb{P}^2 \smallsetminus B)$ for all irreducible plane sextics $B \subset \mathbb{P}^2$ with simple singularities for which $\pi$ is known to admit a dihedral quotient $\mathbb{D}_{10}$. All groups found are shown to be finite, two of them being of large order: 960 and 21600.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 65-91

Dates
Received: 2 November 2007
Revised: 13 June 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448012

Digital Object Identifier
doi:10.2969/aspm/05610065

Mathematical Reviews number (MathSciNet)
MR2604077

Zentralblatt MATH identifier
1193.14037

Subjects
Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14H45: Special curves and curves of low genus

Keywords
Plane sextic non-torus sextic fundamental group dihedral covering

Citation

Degtyarev, Alex. On irreducible sextics with non-abelian fundamental group. Singularities — Niigata–Toyama 2007, 65--91, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610065. https://projecteuclid.org/euclid.aspm/1543448012


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