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This article is cited in 5 scientific papers (total in 5 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 $\sigma\colon V\to{\mathbb P}^M$, $M\ge5$,
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.
DOI:
https://doi.org/10.4213/im4071
 Full text:
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English version:
Izvestiya: Mathematics, 2010, 74:5, 925–991
Bibliographic databases:
     
UDC:
512.7
MSC: 14E05, 14J45, 14J50
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
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http://mi.mathnet.ru/eng/izv4071https://doi.org/10.4213/im4071 http://mi.mathnet.ru/eng/izv/v74/i5/p45
Citing articles on Google Scholar:
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Russian articles,
English articles
This publication is cited in the following articles:
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A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845
 -
A. V. Pukhlikov, “Birationally rigid Fano complete intersections. II”, J. Reine Angew. Math., 688 (2014), 209–218
-
A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150
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Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1-2 (2016), 721–782
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A. V. Pukhlikov, “Birational geometry of singular Fano double spaces of index two”, Sb. Math., 212:4 (2021), 551–566
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