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Birationally rigid varieties with a pencil of Fano double covers. I

Aleksandr V. Pukhlikov
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Abstract

We prove that a general Fano fibration $π\colon V\to {\mathbb P}^1$, the fiber of which is a double Fano hypersurface of index 1, is birationally superrigid provided it is sufficiently twisted over the base. In particular, on $V$ there are no other structures of a rationally connected fibration. The proof is based on the method of maximal singularities.

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Aleksandr V. Pukhlikov. 2003-10-17. Birationally rigid varieties with a pencil of Fano double covers. I. https://arxiv.org/abs/math/0310270

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