Abstract
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.
Citation
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. https://doi.org/10.2969/jmsj/06720663
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