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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 4, Pages 889–906 (Mi izv932)  

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


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.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:1, 169–184

Bibliographic databases:

UDC: 512.7+515.1
MSC: 14H30, 57M05
Received: 16.01.1992

Citation: Vik. S. Kulikov, “On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$”, Izv. RAN. Ser. Mat., 56:4 (1992), 889–906; Russian Acad. Sci. Izv. Math., 41:1 (1993), 169–184

Citation in format AMSBIB
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\by Vik.~S.~Kulikov
\paper On the Lefschetz theorem for the complement of a curve in $\mathbf P^2$
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
\issue 4
\pages 889--906
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1993IzMat..41..169K}
\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 1
\pages 169--184
\crossref{https://doi.org/10.1070/IM1993v041n01ABEH002254}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ichiro Shimada, “On the fundamental group of the complement of a divisor in a homogeneous space”, Math Z, 220:1 (1995), 445  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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