Birational geometry of singular Fano hypersurfaces of index two

For a Zariski general (regular) hypersurface V of degree M in the (M + 1)-dimensional projective space, where M >= 16, with at most quadratic singularities of rank >= 13, we give a complete description of the structures of rationally connected (or Fano-Mori) fibre space: every such structure over a positive-dimensional base is a pencil of hyperplane sections. This implies, in particular, that V is non-rational and its groups of birational and biregular automorphisms coincide: BirV = AutV. The set of non-regular hypersurfaces has codimension at least 1/2 (M - 11)(M - 10) - 10 in the natural parameter space.