Geodesic
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

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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. 
@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},
     publisher = {mathdoc},
     volume = {40},
     number = {2},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_40_2_a6/}
}
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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/