Birational geometry of Fano hypersurfaces of index two

Abstract

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 and its group of birational self-maps coincides with the group of biregular automorphisms and for that reason is trivial. The proof is based on the techniques of the method of maximal singularities and inversion of adjunction.

Locations

• Mathematische Annalen - View - PDF