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VOL. 56 | 2009 A proof of a conjecture of Degtyarev on non-torus plane sextics
Christophe Eyral, Mutsuo Oka

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

Abstract

A $\mathbb{D}_{10}$-sextic is an irreducible sextic $C \subset \mathbb{CP}^2$ with simple singularities such that the fundamental group $\pi_1 (\mathbb{CP}^2 \setminus C)$ factors to the dihedral group $\mathbb{D}_{10}$. A $\mathbb{D}_{10}$-sextic is not of torus type. In this paper, we show that if $C$ is a $\mathbb{D}_{10}$-sextic with the set of singularities $4\mathbf{A}_4$ or $4\mathbf{A}_4 \oplus \mathbf{A}_1$, then $\pi_1 (\mathbb{CP}^2 \setminus C)$ is isomorphic to $\mathbb{D}_{10} \times \mathbb{Z}/3\mathbb{Z}$. This positively answers a conjecture by Degtyarev.

Information

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

zbMATH: 1193.14039
MathSciNet: MR2604079

Digital Object Identifier: 10.2969/aspm/05610109

Subjects:
Primary: 14H30
Secondary: 14H20, 14H45, 14H50

Rights: Copyright © 2009 Mathematical Society of Japan

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