Birational geometry of algebraic varieties fibred into Fano double spaces

Pukhlikov, AV (2017) Birational geometry of algebraic varieties fibred into Fano double spaces. IZVESTIYA MATHEMATICS, 81 (3). pp. 618-644.

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Abstract

We develop the quadratic technique of proving birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base. As an application, we prove birational rigidity of generic fibrations into Fano double spaces of dimension $M\geqslant 4$ and index one over a rationally connected base of dimension at most $\frac12 (M-2)(M-1)$. An estimate for the codimension of the subset of hypersurfaces of a given degree in the projective space with a positive-dimensional singular set is obtained, which is close to the optimal one.

Item Type:	Article
Additional Information:	30 pages, the final version
Uncontrolled Keywords:	Fano-Mori fibre space, Fano variety, maximal singularity, birational map, linear system
Depositing User:	Symplectic Admin
Date Deposited:	20 Dec 2017 09:04
Last Modified:	27 Jun 2023 01:10
DOI:	10.1070/IM8493
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3013962