Geodesic
Birationally rigid varieties with a pencil of Fano double covers. III
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 335-368 Cet article a éte moissonné depuis la source Math-Net.Ru

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The study of the birational geometry of Fano fibre spaces $\pi\colon V\to\mathbb P^1$ with fibre that is a Fano double hypersurface of index 1 is completed. For each family of these varieties either the birational rigidity is proved or non-trivial structures of Fano fibre spaces are explicitly produced. A new linear method of the study of movable systems on Fano fibre spaces $V/\mathbb P^1$ is developed. Bibliography: 17 titles. 
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A. V. Pukhlikov. Birationally rigid varieties with a pencil of Fano double covers. III. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 335-368. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a2/

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