Izvestiya. Mathematics, Tome 40 (1993) no. 2, pp. 443-454
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Vik. S. Kulikov. On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$. Izvestiya. Mathematics, Tome 40 (1993) no. 2, pp. 443-454. http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a6/
@article{IM2_1993_40_2_a6,
author = {Vik. S. Kulikov},
title = {On~the~structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$},
journal = {Izvestiya. Mathematics},
pages = {443--454},
year = {1993},
volume = {40},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a6/}
}
TY - JOUR
AU - Vik. S. Kulikov
TI - On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$
JO - Izvestiya. Mathematics
PY - 1993
SP - 443
EP - 454
VL - 40
IS - 2
UR - http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a6/
LA - en
ID - IM2_1993_40_2_a6
ER -
%0 Journal Article
%A Vik. S. Kulikov
%T On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$
%J Izvestiya. Mathematics
%D 1993
%P 443-454
%V 40
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a6/
%G en
%F IM2_1993_40_2_a6
This paper studies the fundamental group of the complement of an algebraic curve $D=\bigcup D_i$, in $\mathbf C^2$. It is proved that $\pi_1(\mathbf C^2\setminus D)$ decomposes into the direct product of the groups $\pi_1(\mathbf C^2\setminus D_i)$ if for all $i$ and $j$, $i\not= j$, the curves $D_i$ and $D_j$ do not intersect at infinity and in a neighborhood of any point of $D_i\cap D_j$ the curve $D$ is a divisor with normal crossings.
