On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$
Izvestiya. Mathematics , Tome 41 (1993) no. 1, pp. 169-184.

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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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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/

[1] Clemens C. H., “Degeneration of Kähler manifolds”, Duke Math. J., 44:2 (1977), 215–290 | DOI | MR | Zbl

[2] Kempf G., Knudsen F., Mumford D., Saint-Donat B., Toroidal embeddings, Lect. Notes in Math., 339, Springer-Verlag, 1973 | MR | Zbl

[3] Kulikov Vik. S., “Fundamentalnaya gruppa dopolneniya k giperpoverkhnosti v $\mathbf{C}^n$”, Izv. AN SSSR. Ser. matem., 55:2 (1991), 407–428 | MR | Zbl

[4] Kulikov Vik. S., “O strukture fundamentalnoi gruppy dopolneniya k algebraicheskim krivym v $\mathbf{C}^2$”, Izv. AN SSSR. Ser. matem., 56:2 (1992), 469–481 | MR

[5] Nori M., “Zariski's conjecture and related problems”, Ann. Sci. École Norm. Sup. (4), 16:2 (1983), 305–344, 4e serie | MR | Zbl

[6] Zariski O., Algebraic surfaces, Springer-Verlag, Berlin, 1971 | MR | Zbl