Birationally rigid Fano fibre spaces. II



Pukhlikov, A
(2015) Birationally rigid Fano fibre spaces. II. Izvestiya: Mathematics, 79 (4). pp. 809-837.

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Abstract

In this paper we prove birational rigidity of large classes of Fano-Mori fibre spaces over a base of arbitrary dimension, bounded from above by a constant that depends on the dimension of the fibre only. In order to do that, we first show that if every fibre of a Fano-Mori fibre space satisfies certain natural conditions, then every birational map onto another Fano-Mori fibre space is fibre-wise. After that we construct large classes of fibre spaces (into Fano double spaces of index one and into Fano hypersurfaces of index one) which satisfy those conditions.

Item Type: Article
Additional Information: 31 pages
Uncontrolled Keywords: Fano-Mori fibre space, birational rigidity, maximal singularity, hypertangent divisor, log canonical singularity, linear system, canonical class
Subjects: ?? QA ??
Depositing User: Symplectic Admin
Date Deposited: 21 Jun 2016 08:19
Last Modified: 26 Jun 2023 22:04
DOI: 10.1070/IM2015v079n04ABEH002762
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001756

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