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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 5, Pages 974–1025 (Mi izv2189)  

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

The Castelnuovo–Enriques contraction theorem for arbitrary dimension

B. G. Moishezon


Abstract: In the present article we show that the $n$-dimensional generalization of the Castelnuovo–Enriques theorem concerning exceptional curves of the first kind on algebraic surfaces is valid in the category of minischemes over any algebraically closed field. The following result is deduced as a corollary: for every $n$-dimensional compact complex manifold $Y$ with $n$ algebraically independent meromorphic functions there exists a nonsingular minischeme $V$ over the complex field such that the complex manifold $V_\mathbf C$ canonically corresponding to $V$ coincides with $Y^*$.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:5, 917–966

Bibliographic databases:

UDC: 513.6
MSC: 14J28, 32A20, 32Q55, 14Hxx, 14J50, 14A10
Received: 17.03.1969

Citation: B. G. Moishezon, “The Castelnuovo–Enriques contraction theorem for arbitrary dimension”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 974–1025; Math. USSR-Izv., 3:5 (1969), 917–966

Citation in format AMSBIB
\Bibitem{Moi69}
\by B.~G.~Moishezon
\paper The Castelnuovo--Enriques contraction theorem for arbitrary dimension
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 5
\pages 974--1025
\mathnet{http://mi.mathnet.ru/izv2189}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=260749}
\zmath{https://zbmath.org/?q=an:0192.57802}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 5
\pages 917--966
\crossref{https://doi.org/10.1070/IM1969v003n05ABEH000810}


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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. V. S. Zhgoon, “On embeddings of universal torsors over del Pezzo surfaces in cones over flag varieties”, Izv. Math., 74:5 (2010), 883–923  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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