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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 1, Pages 203–208 (Mi izv1424)  

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

On the closed cone of curves of algebraic 3-folds

V. V. Shokurov


Abstract: In this paper the author establishes, under natural conditions, the local polyhedrality of the closed cone of curves of a three-dimensional algebraic variety in the part that is negative with respect to the canonical class. In particular, it is shown that there always exists an extremal ray giving a contraction. The results can be used in three-dimensional birational geometry.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 24:1, 193–198

Bibliographic databases:

UDC: 512.7
MSC: Primary 14E30, 14J30; Secondary 14J99
Received: 14.03.1983

Citation: V. V. Shokurov, “On the closed cone of curves of algebraic 3-folds”, Izv. Akad. Nauk SSSR Ser. Mat., 48:1 (1984), 203–208; Math. USSR-Izv., 24:1 (1985), 193–198

Citation in format AMSBIB
\Bibitem{Sho84}
\by V.~V.~Shokurov
\paper On~the closed cone of curves of algebraic 3-folds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 1
\pages 203--208
\mathnet{http://mi.mathnet.ru/izv1424}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=733364}
\zmath{https://zbmath.org/?q=an:0565.14025}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 24
\issue 1
\pages 193--198
\crossref{https://doi.org/10.1070/IM1985v024n01ABEH001223}


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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. V. V. Shokurov, “The nonvanishing theorem”, Math. USSR-Izv., 26:3 (1986), 591–604  mathnet  crossref  mathscinet  zmath
    2. A. A. Borisov, V. V. Shokurov, “Directional Rational Approximations with Some Applications to Algebraic Geometry”, Proc. Steklov Inst. Math., 240 (2003), 66–74  mathnet  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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