Birationally rigid Fano double hypersurfaces

A general Fano double hypersurface $V$ of index 1 $(\sigma\colon V\to Q_m\subset \mathbb P^{M+1}$ is a double cover branched over a smooth divisor $W=W^*_{2l}\subset\mathbb P^{M+1}$, here $m+l=M+1\geqslant 5)$ is proved to be birationally superrigid; in particular, such a hypersurface admits no non-trivial structures of a fibration into uniruled varieties, and it is non-rational. Its groups of birational and biregular automorphisms coincide.