Birational geometry of Fano hypersurfaces of index two
Birational geometry of Fano hypersurfaces of index two
We prove that every non-trivial structure of a rationally connected fibre space on a generic (in the sense of Zariski topology) hypersurface V of degree M in the $$(M+1)$$ -dimensional projective space for $$M\ge 16$$ is given by a pencil of hyperplane sections. In particular, the variety V is non-rational …