Geodesic
Birationally rigid varieties with a pencil of double Fano covers.~I
Sbornik. Mathematics, Tome 195 (2004) no. 7, pp. 1039-1071

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The general Fano fibration $\pi\colon V\to\mathbb P^1$ the fibre of which is a double Fano hypersurface of index 1 is proved to be birationally superrigid, provided it is sufficiently twisted over the base. In particular, there exist on $V$ no other structures of a rationally convex fibration. The proof is based on the method of maximal singularities. 
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     author = {A. V. Pukhlikov},
     title = {Birationally rigid varieties with a pencil of double {Fano} {covers.~I}},
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A. V. Pukhlikov. Birationally rigid varieties with a pencil of double Fano covers.~I. Sbornik. Mathematics, Tome 195 (2004) no. 7, pp. 1039-1071. http://geodesic.mathdoc.fr/item/SM_2004_195_7_a5/