2017/12/23 by Pukhlikov, Aleksandr V.
#14E05 #14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1712.08796
For a Zariski general (regular) hypersurface V of degree M in the (M+1)-dimensional projective space, where M is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures of rationally connected (or Fano-Mori) fibre space: every such structure over a positive-dimensional base is a pencil of hyperplane sections. This implies, in particular, that V is non-rational and its groups of birational and biregular automorphisms coincide. The set of non-regular hypersurfaces has codimension at least \frac12(M-11)(M-10)-10 in the natural parameter space.