This article is cited in 4 scientific papers (total in 4 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
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.
algebraic threefolds, conic bundles, rationality, singularities, invariants, birational transformations, Sarkisov programme, intermediate Jacobian, Prym variety.
|Ministry of Education and Science of the Russian Federation
|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.
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Russian Mathematical Surveys, 2018, 73:3, 375–456
MSC: Primary 14E05, 14J30; Secondary 14E07, 14E30, 14J45
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
\paper The rationality problem for conic bundles
\jour Uspekhi Mat. Nauk
\jour Russian Math. Surveys
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Sh. Mori, Yu. G. Prokhorov, “Threefold extremal curve germs with one non-Gorenstein point”, Izv. Math., 83:3 (2019), 565–612
V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Fano threefolds with infinite automorphism groups”, Izv. Math., 83:4 (2019), 860–907
Yuri G. Prokhorov, “Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I”, Proc. Steklov Inst. Math., 307 (2019), 210–231
Yu. G. Prokhorov, K. A. Shramov, “Finite groups of bimeromorphic selfmaps of uniruled Kähler threefolds”, Izv. Math., 84:5 (2020), 978–1001
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