On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$

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.