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This article is cited in 5 scientific papers (total in 5 papers)
Birational geometry of varieties fibred into complete intersections of codimension two
A. V. Pukhlikov Department of Mathematical Sciences, University of Liverpool
Abstract:
In this paper we prove the birational superrigidity of Fano–Mori fibre spaces
$\pi\colon V\to S$ all of whose fibres are complete intersections of type
$d_1\cdot d_2$ in the projective space ${\mathbb P}^{d_1+d_2}$ satisfying certain
conditions of general position, under the assumption that the fibration $V/S$
is sufficiently twisted over the base (in particular, under the assumption that the
$K$-condition holds). The condition of general position for every fibre guarantees
that the global log canonical threshold is equal to one. This condition also bounds
the dimension of the base $S$ by a constant depending only on the dimension $M$
of the fibre (this constant grows like $M^2/2$ as $M\to\infty$). The fibres and the variety $V$
may have quadratic and bi-quadratic singularities whose rank is bounded below.
Keywords:
Fano variety, Mori fibre space, birational map, birational rigidity, linear system, maximal singularity,
quadratic singularity, bi-quadratic singularity.
Received: 27.01.2021 Revised: 12.06.2021
Citation:
A. V. Pukhlikov, “Birational geometry of varieties fibred into complete intersections of codimension two”, Izv. Math., 86:2 (2022), 334–411
Linking options:
https://www.mathnet.ru/eng/im9146https://doi.org/10.1070/IM9146 https://www.mathnet.ru/eng/im/v86/i2/p128
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Abstract page: | 296 | Russian version PDF: | 42 | English version PDF: | 41 | Russian version HTML: | 115 | References: | 63 | First page: | 8 |
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