The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$
Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 399-418
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $D$ be a complex algebraic hypersurface in $\mathbf C^n$ not passing through the point $o\in\mathbf C^n$. The generators of the fundamental group $\pi_1(\mathbf C^n\setminus D,o)$ and the relations among them are described in terms of the real cone over $D$ with apex at $o$. This description is a generalization to the algebraic case of Wirtinger's corepresentation of the fundamental group of a knot in $\mathbf R^3$. A new proof of Zariski's conjecture about commutativity of the fundamental group $\pi_1(\mathbf P^2\setminus C)$ for a projective nodal curve $C$ is given in the second part of the paper based on the description of the generators and the relations in the group $\pi_1(\mathbf C^n\setminus D)$ obtained in the first part.
@article{IM2_1992_38_2_a8,
author = {Vik. S. Kulikov},
title = {The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$},
journal = {Izvestiya. Mathematics },
pages = {399--418},
publisher = {mathdoc},
volume = {38},
number = {2},
year = {1992},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a8/}
}
Vik. S. Kulikov. The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$. Izvestiya. Mathematics , Tome 38 (1992) no. 2, pp. 399-418. http://geodesic.mathdoc.fr/item/IM2_1992_38_2_a8/