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Russian Mathematical Surveys, 2005, Volume 60, Issue 5, Pages 875–965
DOI: https://doi.org/10.1070/RM2005v060n05ABEH003736 (Mi rm1643) 		 
This article is cited in 49 scientific papers (total in 49 papers)

Birationally rigid Fano varieties

I. A. Cheltsov

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (1050 kB) Citations (49)
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DOI: https://doi.org/10.1070/RM2005v060n05ABEH003736
Abstract: The birational superrigidity and, in particular, the non-rationality of a smooth three-dimensional quartic was proved by V. Iskovskikh and Yu. Manin in 1971, and this led immediately to a counterexample to the three-dimensional Lüroth problem. Since then, birational rigidity and superrigidity have been proved for a broad class of higher-dimensional varieties, among which the Fano varieties occupy the central place. The present paper is a survey of the theory of birationally rigid Fano varieties.
Received: 23.06.2005
Russian version:
Uspekhi Matematicheskikh Nauk, 2005, Volume 60, Issue 5(365), Pages 71–160
DOI: https://doi.org/10.4213/rm1643
Bibliographic databases:
Document Type: Article
UDC: 512.76
MSC: Primary 14J45, 14E05, 14E30; Secondary 14G22, 14J30, 14E07, 14M20, 14M10
Language: English
Original paper language: Russian
Citation: I. A. Cheltsov, “Birationally rigid Fano varieties”, Uspekhi Mat. Nauk, 60:5(365) (2005), 71–160; Russian Math. Surveys, 60:5 (2005), 875–965
Citation in format AMSBIB
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    • This publication is cited in the following 49 articles:
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