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Mat. Sb., 2002, Volume 193, Number 10, Pages 49–74 (Mi msb685)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalized Tsen's theorem and rationally connected Fano fibrations

F. Campanaa, Th. Peternellb, A. V. Pukhlikovc

a Université de Nantes, Département de Mathématiques
b Universität Bayreuth
c Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The existence is proved and an explicit algebraic description is given for sections of a fibration $X/C$ over a curve $C$ whose general fibre is a Fano complete intersection in a product of weighted projective spaces. It is proved also that a fibration $X/\mathbb P^1$ whose general fibre is a smooth Fano threefold is rationally connected.

DOI: https://doi.org/10.4213/sm685

Full text: PDF file (391 kB)
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English version:
Sbornik: Mathematics, 2002, 193:10, 1443–1468

Bibliographic databases:

UDC: 513.6
MSC: 14D06, 14J45
Received: 17.01.2002

Citation: F. Campana, Th. Peternell, A. V. Pukhlikov, “Generalized Tsen's theorem and rationally connected Fano fibrations”, Mat. Sb., 193:10 (2002), 49–74; Sb. Math., 193:10 (2002), 1443–1468

Citation in format AMSBIB
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\paper Generalized Tsen's theorem and rationally connected Fano fibrations
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\yr 2002
\vol 193
\issue 10
\pages 49--74
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1937041}
\zmath{https://zbmath.org/?q=an:1080.14535}
\transl
\jour Sb. Math.
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\vol 193
\issue 10
\pages 1443--1468
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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. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Auel A., Bernardara M., Bolognesi M., “Fibrations in Complete Intersections of Quadrics, Clifford Algebras, Derived Categories, and Rationality Problems”, J. Math. Pures Appl., 102:1 (2014), 249–291  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. Auel A. Bernardara M., “Cycles, Derived Categories, and Rationality”, Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 95, ed. Coskun I. DeFernex T. Gibney A., Amer Mathematical Soc, 2017, 199–266  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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