2013/10/09 by Pukhlikov, Aleksandr
#14E05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1310.2572
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≥ 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.