This article is cited in 4 papers

Generalized Tsen's theorem and rationally connected Fano fibrations

F. Campana^a, Th. Peternell^b, A. V. Pukhlikov<sup>c

a</sup> 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.

UDC: 513.6

MSC: 14D06, 14J45

Received: 17.01.2002

DOI: 10.4213/sm685

 English version: Sbornik: Mathematics, 2002, 193:10, 1443–1468

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