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- Title
Birational geometry of singular Fano hypersurfaces of index two.
- Authors
Pukhlikov, A. V.
- Abstract
For a Zariski general (regular) hypersurface V of degree M in the (M + 1) -dimensional projective space, where M ⩾ 16 , with at most quadratic singularities of rank ⩾ 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: Bir V = Aut V . The set of non-regular hypersurfaces has codimension at least 1 2 (M - 11) (M - 10) - 10 in the natural parameter space.
- Publication
Manuscripta Mathematica, 2020, Vol 161, Issue 1/2, p161
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s00229-018-1075-3