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This article is cited in 17 scientific papers (total in 17 papers)
Birationally rigid Fano fibre spaces. II
A. V. Pukhlikov University of Liverpool
Abstract:
We prove the birational rigidity of large classes of Fano–Mori fibre spaces
over a base of arbitrary dimension bounded above by a constant that
depends only on the dimension of the fibres. To do this, we first show
that if every fibre of a Fano–Mori fibre space satisfies certain natural
conditions, then every birational map onto another such space
is fibrewise. Then we construct large classes of fibre spaces (whose
fibres are either Fano double spaces of index 1 or Fano hypersurfaces
of index 1) satisfying these conditions.
Keywords:
Fano–Mori fibre space, birational rigidity, maximal singularity,
hypertangent divisor, log canonical singularity, linear system, canonical class.
Received: 02.07.2014
Citation:
A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
Linking options:
https://www.mathnet.ru/eng/im8273https://doi.org/10.1070/IM2015v079n04ABEH002762 https://www.mathnet.ru/eng/im/v79/i4/p175
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