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Mat. Sb. (N.S.), 1988, Volume 137(179), Number 2(10), Pages 260–270 (Mi msb1786)  

This article is cited in 5 scientific papers (total in 5 papers)

The fundamental group of the complement of a plane algebraic curve

S. Yu. Orevkov


Abstract: $\pi_1(\mathbf C^2-K)$ is computed, where $K$ is an algebraic curve having only simple double points and satisfying certain restrictions at infinity. These restrictions are satisfied, for example, for a general curve parametrized by polynomials of given degrees, and also for a general curve with given Newton polyhedron. As a corollary, a new proof of the Fulton-Deligne theorem that $\pi_1(\mathbf CP^2-K)$ is abelian is obtained, if $K$ has only simple double points in $\mathbf CP^2$.
Figures: 1.
Bibliography: 7 titles.

Full text: PDF file (736 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 65:1, 267–277

Bibliographic databases:

UDC: 512
MSC: 14H30
Received: 19.08.1987

Citation: S. Yu. Orevkov, “The fundamental group of the complement of a plane algebraic curve”, Mat. Sb. (N.S.), 137(179):2(10) (1988), 260–270; Math. USSR-Sb., 65:1 (1990), 267–277

Citation in format AMSBIB
\Bibitem{Ore88}
\by S.~Yu.~Orevkov
\paper The fundamental group of the complement of a~plane algebraic curve
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 137(179)
\issue 2(10)
\pages 260--270
\mathnet{http://mi.mathnet.ru/msb1786}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=971697}
\zmath{https://zbmath.org/?q=an:0681.14003|0662.14004}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 267--277
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001310}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988CP43500014}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Orevkov, “The commutant of the fundamental group of the complement of a plane algebraic curve”, Russian Math. Surveys, 45:1 (1990), 221–222  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Vik. S. Kulikov, “The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$”, Math. USSR-Izv., 38:2 (1992), 399–418  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. S. Yu. Orevkov, “Rudolph diagrams and an analytic realization of the Vitushkin covering”, Math. Notes, 60:2 (1996), 153–164  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Cheniot D., “Homotopical Variation”, Singularities II: Geometric and Topological Aspects, Contemporary Mathematics, 475, eds. Brasselet J., CisnerosMolina J., Massey D., Seade J., Teissier B., Amer Mathematical Soc, 2008, 11–41  crossref  mathscinet  zmath  isi
    5. Baader S., Kutzschebauch F., Wold E.E., “Knotted Holomorphic Discs in C-2”, J. Reine Angew. Math., 648 (2010), 69–73  crossref  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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