Geodesic
On Chisini's conjecture. II
Izvestiya. Mathematics , Tome 72 (2008) no. 5, pp. 901-913

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We prove that if $S\subset\mathbb P^N$ is a smooth projective surface and $f\colon S\to\mathbb P^2$ is a generic linear projection branched over a cuspidal curve $B\subset\mathbb P^2$, then $S$ is uniquely determined (up to isomorphism) by $B$. 
@article{IM2_2008_72_5_a1,
     author = {Vik. S. Kulikov},
     title = {On {Chisini's} conjecture. {II}},
     journal = {Izvestiya. Mathematics },
     pages = {901--913},
     publisher = {mathdoc},
     volume = {72},
     number = {5},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_5_a1/}
}
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Vik. S. Kulikov. On Chisini's conjecture. II. Izvestiya. Mathematics , Tome 72 (2008) no. 5, pp. 901-913. http://geodesic.mathdoc.fr/item/IM2_2008_72_5_a1/