Birational geometry of Fano direct products

We prove the birational superrigidity of direct products of primitive Fano varieties of the following two types: either is a general hypersurface of degree?, , or is a general double space of index?1, . In particular, every structure of a rationally connected fibre space on? is given by the projection onto a direct factor. The proof is based on the connectedness principle of Shokurov and Koll?r and the technique of hypertangent divisors.

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