Birationally rigid Fano double hypersurfaces

A general Fano double hypersurface V of index 1 (sigma: V --> Q(m) subset o f PM+1 is a double cover branched over a smooth divisor W = W-2 iota* subse t of PM+1, here m + iota = M + 1 greater than or equal to 5) is proved to b e birationally superrigid; in particular, such a hypersurface admits no non -trivial structures of a fibration into uniruled varieties, and it is non-r ational. Its groups of birational and biregular automorphisms coincide.