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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 3, Pages 17–25 (Mi faa308)  

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

Equidistribution of Divisors for Sequences of Holomorphic Curves

I. M. Dektyarev

Vladimir State Pedagogical University

Abstract: We study holomorphic curves in an $n$-dimensional complex manifold on which a family of divisors parametrized by an $m$-dimensional compact complex manifold is given. If, for a given sequence of such curves, their areas (in the induced metric) monotonically tend to infinity, then for every divisor one can define a defect characterizing the deviation of the frequency at which this sequence intersects the divisor from the average frequency (over the set of all divisors). It turns out that, as well as in the classical multidimensional case, the set of divisors with positive defect is very rare. (We estimate how rare it is.) Moreover, the defect of almost all divisors belonging to a linear subsystem is equal to the mean value of the defect over the subsystem, and for all divisors in the subsystem (without any exception) the defect is not less than this mean value.

DOI: https://doi.org/10.4213/faa308

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English version:
Functional Analysis and Its Applications, 2000, 34:3, 172–178

Bibliographic databases:

UDC: 515.16
Received: 18.12.1998

Citation: I. M. Dektyarev, “Equidistribution of Divisors for Sequences of Holomorphic Curves”, Funktsional. Anal. i Prilozhen., 34:3 (2000), 17–25; Funct. Anal. Appl., 34:3 (2000), 172–178

Citation in format AMSBIB
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\by I.~M.~Dektyarev
\paper Equidistribution of Divisors for Sequences of Holomorphic Curves
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 3
\pages 17--25
\mathnet{http://mi.mathnet.ru/faa308}
\crossref{https://doi.org/10.4213/faa308}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1802315}
\zmath{https://zbmath.org/?q=an:0979.32014}
\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 3
\pages 172--178
\crossref{https://doi.org/10.1007/BF02482406}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000165392400002}


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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. I. M. Dektyarev, “A New Notion of Defect for Holomorphic Curves and Their Sequences”, Funct. Anal. Appl., 36:4 (2002), 281–289  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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