Birational geometry of Fano hypersurfaces of index two

Abstract

We prove that every non-trivial structure of a rationally connected fibre space (and so every structure of a Mori-Fano fibre space) on a general (in the sense of Zariski topology) hypersurface of degree $M$ in the $(M+1)$-dimensional projective space for $M\ge 14$ is given by a pencil of hyperplane sections. In particular, the variety $V$ is non-rational and its group of birational self-maps coincide with the group of biregular automorphisms and is therefore trivial. The proof is based on the techniques of the method of maximal singularities and the inversion of adjunction.

50 pages, the complete version

Cited by in corpus (1)

• On birational superrigidity and conditional birational superrigidity of certain Fano hypersurfaces