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Izvestiya: Mathematics, 2015, Volume 79, Issue 4, Pages 809–837
DOI: https://doi.org/10.1070/IM2015v079n04ABEH002762 (Mi im8273) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Birationally rigid Fano fibre spaces. II

A. V. Pukhlikov

University of Liverpool
English version PDF (427 kB) Citations (16)
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DOI: https://doi.org/10.1070/IM2015v079n04ABEH002762
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.
Received: 02.07.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 4, Pages 175–204
DOI: https://doi.org/10.4213/im8273
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: 14E05, 14J45, 14D06, 14M22, 14E30
Language: English
Original paper language: Russian
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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  • https://www.mathnet.ru/eng/im/v79/i4/p175
    Cycle of papers
    This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:453
    Russian version PDF:152
    English version PDF:18
    References:47
    First page:10
     
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