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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 3, Pages 160–188 (Mi izv8493)  

This article is cited in 3 scientific papers (total in 3 papers)

Birational geometry of algebraic varieties fibred into Fano double spaces

A. V. Pukhlikov

University of Liverpool

Abstract: We develop a quadratic technique for proving the birational rigidity of Fano–Mori fibre spaces over a higher-dimensional base. As an application, we prove the birational rigidity of generic fibrations into Fano double spaces of dimension $M\ge 4$ and index $1$ over a rationally connected base of dimension at most $(M-2)(M-1)/2$. We obtain a near-optimal estimate for the codimension of the set of hypersurfaces of a given degree in projective space that have positive-dimensional singular sets.

Keywords: Fano–Mori fibre space, Fano variety, maximal singularity, birational map, linear system.

DOI: https://doi.org/10.4213/im8493

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English version:
Izvestiya: Mathematics, 2017, 81:3, 618–644

Bibliographic databases:

UDC: 512.7
MSC: 14E05, 14J45, 14D06
Received: 17.12.2015
Revised: 18.05.2016

Citation: A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. RAN. Ser. Mat., 81:3 (2017), 160–188; Izv. Math., 81:3 (2017), 618–644

Citation in format AMSBIB
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\pages 160--188
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  • http://mi.mathnet.ru/eng/izv8493
  • https://doi.org/10.4213/im8493
  • http://mi.mathnet.ru/eng/izv/v81/i3/p160

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. V. Pukhlikov, “Factorial hypersurfaces”, Proc. Steklov Inst. Math., 299 (2017), 205–218  mathnet  crossref  crossref  isi  elib
    3. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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