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Izvestiya: Mathematics, 2000, Volume 64, Issue 3, Pages 563–581
DOI: https://doi.org/10.1070/im2000v064n03ABEH000291 (Mi im291) 		 
This article is cited in 25 scientific papers (total in 25 papers)

Birationally rigid Fano fibrations

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (252 kB) Citations (25)
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DOI: https://doi.org/10.1070/im2000v064n03ABEH000291
Abstract: We prove the birational superrigidity of a general Fano fibration $\pi\colon V\to\mathbf P^1$ whose fibre is a Fano hypersurface $W_M\subset\mathbf P^M$ of index 1. If the fibration is sufficiently twisted over the base $\mathbf P^1$, then $V$ has no other structure of a fibration into rationally connected varieties. We also formulate and discuss conjectures on birational rigidity for a large class of Fano varieties and Fano fibrations over a base of arbitrary dimension.
Received: 03.11.1998
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2000, Volume 64, Issue 3, Pages 131–150
DOI: https://doi.org/10.4213/im291
Bibliographic databases:
Document Type: Article
MSC: 14E07, 14J45
Language: English
Original paper language: Russian
Citation: A. V. Pukhlikov, “Birationally rigid Fano fibrations”, Izv. RAN. Ser. Mat., 64:3 (2000), 131–150; Izv. Math., 64:3 (2000), 563–581
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v64/i3/p131
    Cycle of papers
    This publication is cited in the following 25 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:431
    Russian version PDF:186
    English version PDF:9
    References:51
    First page:2
     
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