Geodesic
On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$
Izvestiya. Mathematics, Tome 41 (1993) no. 1, pp. 169-184 
Vik. S. Kulikov. On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$. Izvestiya. Mathematics, Tome 41 (1993) no. 1, pp. 169-184. http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\bar E$ be an irreducible plane curve over the field $\mathbf C$ of complex numbers, let $\widetilde\nu\colon\widetilde E\to E\subset\mathbf P^2$ be the normalization morphism, and let $\bar D$ be an arbitrary curve in $\mathbf P^2$ such that $\bar E\not\subset\bar D$. The main result of this paper says that if $\bar E$ and $\bar D$ intersect transversely, then $\widetilde\nu_*\colon\pi_1(\widetilde E\setminus\widetilde\nu^{-1}(\bar E\cap\bar D))\to\pi(\mathbf P^2\setminus\bar D)$ is an epimorphism.

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