Birational geometry of Fano hypersurfaces of index two

Pukhlikov, AV (2016) Birational geometry of Fano hypersurfaces of index two. Mathematische Annalen, 366 (1-2). pp. 721-782.

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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 $M\geq 16$ 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 niregular automorphisms and for that reason is trivial. The proof is based on the techniques of the method of maximal singularities and inversion of adjunction.

Item Type:	Article
Additional Information:	39 pages
Uncontrolled Keywords:	math.AG, math.AG, 14E05, 14E07
Depositing User:	Symplectic Admin
Date Deposited:	21 Jun 2016 09:15
Last Modified:	19 Jan 2023 07:35
DOI:	10.1007/s00208-015-1345-2
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3001757