Birationally rigid Fano hypersurfaces with isolated singularities

It is proved that a general Fano hypersurface V = V-M subset of P-M of index 1 with isolated singularities in general position is birationally rigid. Hence it cannot be fibred into uniruled varieties of smaller dimension by a rational map, and each Q-Fano variety V' with Picard number 1 birationally equivalent to V is in fact isomorphic to V. In particular, V is non-rational. The group of birational self-maps of V is either {1} or Z/2Z, depending on whether V has a terminal point of the maximum possible multiplicity M - 2: The proof is based on a combination of the method of maximal singularities and the techniques of hypertangent systems with Shokurov's connectedness principle.