RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 2, Pages 407–428 (Mi izv1016)  

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


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.

Full text: PDF file (9004 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1992, 38:2, 399–418

Bibliographic databases:

Document Type: Article
UDC: 512.7+515.1
MSC: Primary 14J70, 57M05; Secondary 57M25
Received: 05.12.1989

Citation: Vik. S. Kulikov, “The fundamental group of the scomplement to a hypersurface in $\mathbf C^n$”, Izv. Akad. Nauk SSSR Ser. Mat., 55:2 (1991), 407–428; 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 Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 2
\pages 407--428
\mathnet{http://mi.mathnet.ru/izv1016}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1133305}
\zmath{https://zbmath.org/?q=an:0802.14007}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38..399K}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 2
\pages 399--418
\crossref{https://doi.org/10.1070/IM1992v038n02ABEH002205}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992HR86300009}


Linking options:
  • http://mi.mathnet.ru/eng/izv1016
  • http://mi.mathnet.ru/eng/izv/v55/i2/p407

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Generalized and local Jacobian problems”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 351–365  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. Vik. S. Kulikov, “On the structure of the fundamental group of the complement of algebraic curves in $\mathbf C^2$”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 443–454  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. Vik. S. Kulikov, “A geometric realization of $C$-groups”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 197–206  mathnet  crossref  mathscinet  zmath  isi
    6. 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
    7. Vik. S. Kulikov, “On Chisini's conjecture”, Izv. Math., 63:6 (1999), 1139–1170  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Anar Akhmedov, B. Doug Park, “Exotic smooth structures on small 4-manifolds with odd signatures”, Invent math, 2010  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:199
    Full text:76
    References:39
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019