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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 2, Pages 469–480 (Mi izv952)  

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

On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$

Vik. S. Kulikov


Abstract: This paper studies the fundamental group of the complement of an algebraic curve $D=\bigcup D_i$, in $\mathbf C^2$. It is proved that $\pi_1(\mathbf C^2\setminus D)$ decomposes into the direct product of the groups $\pi_1(\mathbf C^2\setminus D_i)$ if for all $i$ and $j$, $i\not= j$, the curves $D_i$ and $D_j$ do not intersect at infinity and in a neighborhood of any point of $D_i\cap D_j$ the curve $D$ is a divisor with normal crossings.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 40:2, 443–454

Bibliographic databases:

Document Type: Article
UDC: 512.7+515.1
MSC: 14H30
Received: 18.06.1991

Citation: Vik. S. Kulikov, “On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$”, Izv. RAN. Ser. Mat., 56:2 (1992), 469–480; Russian Acad. Sci. Izv. Math., 40:2 (1993), 443–454

Citation in format AMSBIB
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\by Vik.~S.~Kulikov
\paper On~the~structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 2
\pages 469--480
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\zmath{https://zbmath.org/?q=an:0783.14009}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..40..443K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 40
\issue 2
\pages 443--454
\crossref{https://doi.org/10.1070/IM1993v040n02ABEH002172}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LD21400007}


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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. Vik. S. Kulikov, “On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 169–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Vik. S. Kulikov, “Alexander polynomials of plane algebraic curves”, Russian Acad. Sci. Izv. Math., 42:1 (1994), 67–89  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Vik. S. Kulikov, “On the fundamental groups of complements of toral curves”, Izv. Math., 61:1 (1997), 89–112  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Vik. S. Kulikov, “On Chisini's conjecture”, Izv. Math., 63:6 (1999), 1139–1170  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. 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
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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