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Russian Academy of Sciences. Izvestiya Mathematics, 1993, Volume 41, Issue 1, Pages 169–184
DOI: https://doi.org/10.1070/IM1993v041n01ABEH002254
(Mi im932)
 

This article is cited in 1 scientific paper (total in 1 paper)

On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$

Vik. S. Kulikov
References:
Abstract: Let $\bar E$ be an irreducible plane curve over the field $\mathbf C$ of complex numbers, let $\widetilde\nu\colon\widetilde E\to E\subset\mathbf P^2$ be the normalization morphism, and let $\bar D$ be an arbitrary curve in $\mathbf P^2$ such that $\bar E\not\subset\bar D$. The main result of this paper says that if $\bar E$ and $\bar D$ intersect transversely, then $\widetilde\nu_*\colon\pi_1(\widetilde E\setminus\widetilde\nu^{-1}(\bar E\cap\bar D))\to\pi(\mathbf P^2\setminus\bar D)$ is an epimorphism.
Received: 16.01.1992
Bibliographic databases:
Document Type: Article
UDC: 512.7+515.1
MSC: 14H30, 57M05
Language: English
Original paper language: Russian
Citation: 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
Citation in format AMSBIB
\Bibitem{Kul92}
\by Vik.~S.~Kulikov
\paper On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 1
\pages 169--184
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\crossref{https://doi.org/10.1070/IM1993v041n01ABEH002254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1208156}
\zmath{https://zbmath.org/?q=an:0798.14008}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..169K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1993LZ84700009}
Linking options:
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  • https://doi.org/10.1070/IM1993v041n01ABEH002254
  • https://www.mathnet.ru/eng/im/v56/i4/p889
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:254
    Russian version PDF:83
    English version PDF:18
    References:50
    First page:2
     
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