Geodesic
Generalized Tsen's theorem and rationally connected Fano fibrations
Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1443-1468

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2002_193_10_a2,
     author = {F. Campana and Th. Peternell and A. V. Pukhlikov},
     title = {Generalized {Tsen's} theorem and rationally connected {Fano} fibrations},
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     number = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_10_a2/}
}
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F. Campana; Th. Peternell; A. V. Pukhlikov. Generalized Tsen's theorem and rationally connected Fano fibrations. Sbornik. Mathematics, Tome 193 (2002) no. 10, pp. 1443-1468. http://geodesic.mathdoc.fr/item/SM_2002_193_10_a2/