Open Access
April, 2015 Classification of the fundamental groups of join-type curves of degree seven
Christophe EYRAL, Mutsuo OKA
J. Math. Soc. Japan 67(2): 663-698 (April, 2015). DOI: 10.2969/jmsj/06720663


We compute the fundamental groups $\pi_1(\mathbb{P}^2\setminus C)$ for all complex curves $C$ of degree $7$ defined by an equation of the form

$$\prod_{j=1}^\ell (Y-\beta_j Z)^{\nu_j} = c\cdot\prod_{i=1}^m (X-\alpha_i Z)^{\lambda_i},$$

where $\sum_{j=1}^\ell \nu_j=\sum_{i=1}^m \lambda_i$ is the degree of the curve, $c\in\mathbb{R}\setminus \{0\}$, and $\beta_1,\ldots,\beta_\ell$ (respectively $\alpha_1,\ldots,\alpha_m$) mutually distinct real numbers.


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Christophe EYRAL. Mutsuo OKA. "Classification of the fundamental groups of join-type curves of degree seven." J. Math. Soc. Japan 67 (2) 663 - 698, April, 2015.


Published: April, 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1328.14051
MathSciNet: MR3340191
Digital Object Identifier: 10.2969/jmsj/06720663

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

Keywords: fundamental group , Monodromy , plane curves , Zariski–van Kampen pencil method

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 2 • April, 2015
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