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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
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.
Received: 15.12.2017 Revised: 22.03.2018
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
Linking options:
https://www.mathnet.ru/eng/rm9811https://doi.org/10.1070/RM9811 https://www.mathnet.ru/eng/rm/v73/i3/p3
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Abstract page: | 925 | Russian version PDF: | 159 | English version PDF: | 63 | References: | 83 | First page: | 46 |
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