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Mat. Sb. (N.S.), 1985, Volume 127(169), Number 1(5), Pages 55–71 (Mi msb1957)  

This article is cited in 2 scientific papers (total in 2 papers)

On hyperbolic embedding of complements of divisors and the limiting behavior of the Kobayashi–Rroyden metric

M. G. Zaidenberg


Abstract: In the following three cases criteria are found for complements of divisors in compact complex manifolds to be hyperbolically embedded in the sense of Kobayashi: for divisors with normal crossings, for arbitrary divisors in complex surfaces, and for unions of hyperplanes in projective space. A criterion is given for two-dimensional polynomial polyhedra to be hyperbolically embedded, and Iitaka's conjecture about conditions for hyperbolicity of the complement of a set of projective lines is confirmed. Upper semicontinuity is proved for the Kobayashi–Royden pseudometrics and Kobayashi–Eisenman pseudovolumes of a family of complex manifolds containing degenerate fibers, and conditions are given under which the hyperbolic length (volume) on the smooth part of a degenerate fiber is the limit of the hyperbolic length (volume) on the nonsingular fibers.
Bibliography: 28 titles.

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English version:
Mathematics of the USSR-Sbornik, 1986, 55:1, 55–70

Bibliographic databases:

UDC: 517.5
MSC: 32H20
Received: 25.04.1984

Citation: M. G. Zaidenberg, “On hyperbolic embedding of complements of divisors and the limiting behavior of the Kobayashi–Rroyden metric”, Mat. Sb. (N.S.), 127(169):1(5) (1985), 55–71; Math. USSR-Sb., 55:1 (1986), 55–70

Citation in format AMSBIB
\Bibitem{Zai85}
\by M.~G.~Zaidenberg
\paper On hyperbolic embedding of complements of divisors and the limiting behavior of the Kobayashi--Rroyden metric
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 127(169)
\issue 1(5)
\pages 55--71
\mathnet{http://mi.mathnet.ru/msb1957}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791317}
\zmath{https://zbmath.org/?q=an:0593.32016|0578.32035}
\transl
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 1
\pages 55--70
\crossref{https://doi.org/10.1070/SM1986v055n01ABEH002991}


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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. M. G. Zaidenberg, “Isotrivial families of curves on affine surfaces and characterization of the affine plane”, Math. USSR-Izv., 30:3 (1988), 503–532  mathnet  crossref  mathscinet  zmath
    2. M. G. Zaidenberg, “Stability of hyperbolic imbeddedness and construction of examples”, Math. USSR-Sb., 63:2 (1989), 351–361  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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