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Russian Mathematical Surveys, 2007, Volume 62, Issue 5, Pages 857–942
DOI: https://doi.org/10.1070/RM2007v062n05ABEH004454 (Mi rm8505) 		 
This article is cited in 16 scientific papers (total in 17 papers)

Birationally rigid varieties. I. Fano varieties

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (971 kB) Citations (17)
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DOI: https://doi.org/10.1070/RM2007v062n05ABEH004454
Abstract: The theory of birational rigidity of rationally connected varieties generalises the classical rationality problem. This paper gives a survey of the current state of this theory and traces its history from Noether's theorem and the Lüroth problem to the latest results on the birational superrigidity of higher-dimensional Fano varieties. The main components of the method of maximal singularities are considered.
Received: 03.06.2007
Russian version:
Uspekhi Matematicheskikh Nauk, 2007, Volume 62, Issue 5(377), Pages 15–106
DOI: https://doi.org/10.4213/rm8505
Bibliographic databases:
Document Type: Article
UDC: 512.7
MSC: Primary 14J45, 14E08, 14E05; Secondary 14C20, 14G22, 14M10, 14M20
Language: English
Original paper language: Russian
Citation: A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Uspekhi Mat. Nauk, 62:5(377) (2007), 15–106; Russian Math. Surveys, 62:5 (2007), 857–942
Citation in format AMSBIB
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    Cycle of papers
    This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:80
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