Birational geometry of Fano direct products
Birational geometry of Fano direct products
We prove birational superrigidity of direct products $V=F_1\times...\times F_K$ of primitive Fano varieties of the following two types: either $F_i\subset{\mathbb P}^M$ is a general hypersurface of degree $M$, $M\geq 6$, or $F_i\stackrel{\sigma}{\to}{\mathbb P}^M$ is a general double space of index 1, $M\geq 3$. In particular, each structure of a rationally …