Advanced Studies in Pure Mathematics

A plane sextic with finite fundamental group

Alex Degtyarev and Mutsuo Oka

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Abstract

We analyze irreducible plane sextics whose fundamental group factors to $\mathbb{D}_{14}$. We produce explicit equations for all curves and show that, in the simplest case of the set of singularities $3\mathbf{A}_6$, the group is $\mathbb{D}_{14} \times \mathbb{Z}_3$.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 93-108

Dates
Received: 2 November 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448013

Digital Object Identifier
doi:10.2969/aspm/05610093

Mathematical Reviews number (MathSciNet)
MR2604078

Zentralblatt MATH identifier
1193.14038

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; Oka, Mutsuo. A plane sextic with finite fundamental group. Singularities — Niigata–Toyama 2007, 93--108, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610093. https://projecteuclid.org/euclid.aspm/1543448013


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