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This article is cited in 9 scientific papers (total in 9 papers)
Birational geometry of Fano double spaces of index two
A. V. Pukhlikovab a Steklov Mathematical Institute, Russian Academy of Sciences
b University of Liverpool
Abstract:
We study birational geometry of Fano varieties realized as double covers $\sigma\colon V\to{\mathbb P}^M$, $M\geqslant5$, branched over generic smooth hypersurfaces $W=W_{2(M-1)}$ of degree $2(M-1)$. We prove that the only structures of a rationally connected fibre space on $V$ are pencil-subsystems of the free linear system $|{-\frac12K_V}|$. The groups of birational and biregular self-maps of $V$ coincide: $\operatorname{Bir}V=\operatorname{Aut}V$.
Keywords:
birational map, Fano variety, maximal singularity, rationally connected fibre space, birational self-map.
Received: 26.12.2008 Revised: 29.05.2009
Citation:
A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. RAN. Ser. Mat., 74:5 (2010), 45–114; Izv. Math., 74:5 (2010), 925–991
Linking options:
https://www.mathnet.ru/eng/im4071https://doi.org/10.1070/IM2010v074n05ABEH002512 https://www.mathnet.ru/eng/im/v74/i5/p45
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Abstract page: | 581 | Russian version PDF: | 170 | English version PDF: | 8 | References: | 47 | First page: | 11 |
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