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Russian Mathematical Surveys, 2018, Volume 73, Issue 3, Pages 375–456
DOI: https://doi.org/10.1070/RM9811 (Mi rm9811) 		 
This article is cited in 17 scientific papers (total in 17 papers)

The rationality problem for conic bundles

Yu. G. Prokhorovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Laboratory of Algebraic Geometry and its Applications, National Research University Higher School of Economics
English version PDF (1356 kB) Citations (17)
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DOI: https://doi.org/10.1070/RM9811
Abstract: This expository paper is concerned with the rationality problem for three-dimensional algebraic varieties with a conic bundle structure. The main methods of this theory are discussed, proofs of certain principal results are sketched, and some recent achievements are presented. Many open problems are also stated.
Bibliography: 209 titles.
Keywords: algebraic threefolds, conic bundles, rationality, singularities, invariants, birational transformations, Sarkisov programme, intermediate Jacobian, Prym variety.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
This work was partially supported by the Russian Academic Excellence Project ``5-100''. The paper was written while the author was visiting the Max Planck Institute for Mathematics (Bonn). He would like to thank the institute for the invitation and the excellent working conditions.
Received: 15.12.2017
Revised: 22.03.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2018, Volume 73, Issue 3(441), Pages 3–88
DOI: https://doi.org/10.4213/rm9811
Bibliographic databases:
Document Type: Article
UDC: 512.776
MSC: Primary 14E05, 14J30; Secondary 14E07, 14E30, 14J45
Language: English
Original paper language: Russian
Citation: Yu. G. Prokhorov, “The rationality problem for conic bundles”, Uspekhi Mat. Nauk, 73:3(441) (2018), 3–88; Russian Math. Surveys, 73:3 (2018), 375–456
Citation in format AMSBIB
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    References:83
    First page:46
     
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