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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 4, Pages 175–204 (Mi izv8273)  

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

Birationally rigid Fano fibre spaces. II

A. V. Pukhlikov

University of Liverpool

Abstract: We prove the birational rigidity of large classes of Fano–Mori fibre spaces over a base of arbitrary dimension bounded above by a constant that depends only on the dimension of the fibres. To do this, we first show that if every fibre of a Fano–Mori fibre space satisfies certain natural conditions, then every birational map onto another such space is fibrewise. Then we construct large classes of fibre spaces (whose fibres are either Fano double spaces of index 1 or Fano hypersurfaces of index 1) satisfying these conditions.

Keywords: Fano–Mori fibre space, birational rigidity, maximal singularity, hypertangent divisor, log canonical singularity, linear system, canonical class.

DOI: https://doi.org/10.4213/im8273

Full text: PDF file (668 kB)
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English version:
Izvestiya: Mathematics, 2015, 79:4, 809–837

Bibliographic databases:

UDC: 512.7
MSC: 14E05, 14J45, 14D06, 14M22, 14E30
Received: 02.07.2014

Citation: A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. RAN. Ser. Mat., 79:4 (2015), 175–204; Izv. Math., 79:4 (2015), 809–837

Citation in format AMSBIB
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\paper Birationally rigid Fano fibre spaces. II
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  • http://mi.mathnet.ru/eng/izv8273
  • https://doi.org/10.4213/im8273
  • http://mi.mathnet.ru/eng/izv/v79/i4/p175

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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Fontanari C., Martinelli D., “A Remark on Rationally Connected Varieties and Mori Dream Spaces”, Proc. Edinb. Math. Soc., 62:1 (2019), 259–263  crossref  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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