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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 5, Pages 45–114 (Mi izv4071)  

This article is cited in 4 scientific papers (total in 4 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: PDF file (959 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:5, 925–991

Bibliographic databases:

Document Type: Article
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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. V. Pukhlikov, “Birationally rigid Fano complete intersections. II”, J. Reine Angew. Math., 688 (2014), 209–218  crossref  mathscinet  zmath  isi  scopus
    3. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    4. Pukhlikov A.V., “Birational geometry of Fano hypersurfaces of index two”, Math. Ann., 366:1-2 (2016), 721–782  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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