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Mathematics of the USSR-Izvestiya, 1992, Volume 38, Issue 2, Pages 399–418
DOI: https://doi.org/10.1070/IM1992v038n02ABEH002205
(Mi im1016)
 

This article is cited in 8 scientific papers (total in 8 papers)

The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$

Vik. S. Kulikov
References:
Abstract: Let $D$ be a complex algebraic hypersurface in $\mathbf C^n$ not passing through the point $o\in\mathbf C^n$. The generators of the fundamental group $\pi_1(\mathbf C^n\setminus D,o)$ and the relations among them are described in terms of the real cone over $D$ with apex at $o$. This description is a generalization to the algebraic case of Wirtinger's corepresentation of the fundamental group of a knot in $\mathbf R^3$. A new proof of Zariski's conjecture about commutativity of the fundamental group $\pi_1(\mathbf P^2\setminus C)$ for a projective nodal curve $C$ is given in the second part of the paper based on the description of the generators and the relations in the group $\pi_1(\mathbf C^n\setminus D)$ obtained in the first part.
Received: 05.12.1989
Bibliographic databases:
Document Type: Article
UDC: 512.7+515.1
MSC: Primary 14J70, 57M05; Secondary 57M25
Language: English
Original paper language: Russian
Citation: Vik. S. Kulikov, “The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$”, Math. USSR-Izv., 38:2 (1992), 399–418
Citation in format AMSBIB
\Bibitem{Kul91}
\by Vik.~S.~Kulikov
\paper The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 2
\pages 399--418
\mathnet{http://mi.mathnet.ru//eng/im1016}
\crossref{https://doi.org/10.1070/IM1992v038n02ABEH002205}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1133305}
\zmath{https://zbmath.org/?q=an:0802.14007}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..399K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1992HR86300009}
Linking options:
  • https://www.mathnet.ru/eng/im1016
  • https://doi.org/10.1070/IM1992v038n02ABEH002205
  • https://www.mathnet.ru/eng/im/v55/i2/p407
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:383
    Russian version PDF:138
    English version PDF:20
    References:83
    First page:1
     
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