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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 5, Pages 63–76 (Mi izv1579)  

This article is cited in 10 scientific papers (total in 10 papers)

On Chisini's conjecture. II

Vik. S. Kulikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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 $B$.

DOI: https://doi.org/10.4213/im1579

Full text: PDF file (511 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:5, 901–913

Bibliographic databases:

UDC: 512.7+515.1
MSC: 14E22, 14N05, 14J25
Received: 10.10.2006

Citation: Vik. S. Kulikov, “On Chisini's conjecture. II”, Izv. RAN. Ser. Mat., 72:5 (2008), 63–76; Izv. Math., 72:5 (2008), 901–913

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Vik. S. Kulikov, “Hurwitz curves”, Russian Math. Surveys, 62:6 (2007), 1043–1119  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. S. Kulikov, Vik. S. Kulikov, “On complete degenerations of surfaces with ordinary singularities in $\mathbb P^3$”, Sb. Math., 201:1 (2010), 129–158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Liedtke Ch., “Fundamental groups of Galois closures of generic projections”, Trans. Amer. Math. Soc., 362:4 (2010), 2167–2188  crossref  mathscinet  zmath  isi  scopus
    4. Eliyahu M., Garber D., Teicher M., “A conjugation-free geometric presentation of fundamental groups of arrangements”, Manuscripta Math., 133:1-2 (2010), 247–271  crossref  mathscinet  zmath  isi  scopus
    5. Eliyahu M., Garber D., Teicher M., “A conjugation-free geometric presentation of fundamental groups of arrangements II: expansion and some properties”, Internat. J. Algebra Comput., 21:5 (2011), 775–792  crossref  mathscinet  zmath  isi  elib  scopus
    6. Friedman M., Leyenson M., Shustin E., “On ramified covers of the projective plane I: interpreting Segre's theory”, Internat. J. Math., 22:5 (2011), 619–653  crossref  mathscinet  zmath  isi  elib  scopus
    7. Kaminski J.-Y., Sepulcre Ya., “Using discriminant curves to recover a surface of $\mathbb P^4$ from two generic linear projections”, ISSAC 2011—Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, ed. Leykin A., Assoc Computing Machinery, New York, 2011, 187–192  crossref  mathscinet  zmath  isi  scopus
    8. Friedman M. Lehman R. Leyenson M. Teicher M., “On ramified covers of the projective plane II: generalizing Segre's theory”, J. Eur. Math. Soc. (JEMS), 14:3 (2012), 971–996  crossref  mathscinet  zmath  isi  scopus
    9. Bogomolov F., Kulikov Vik.S., “On the irreducibility of Hilbert scheme of surfaces of minimal degree”, Cent. Eur. J. Math., 11:2 (2013), 254–263  crossref  mathscinet  zmath  isi  elib  scopus
    10. Oba T., “Compact Stein Surfaces as Branched Covers With Same Branch Sets”, Algebr. Geom. Topol., 18:3 (2018), 1733–1751  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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