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Uspekhi Mat. Nauk, 2018, Volume 73, Issue 3(441), Pages 3–88 (Mi umn9811)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

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.


DOI: https://doi.org/10.4213/rm9811

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English version:
Russian Mathematical Surveys, 2018, 73:3, 375–456

Bibliographic databases:

ArXiv: 1712.05564
Document Type: Article
UDC: 512.776
MSC: Primary 14E05, 14J30; Secondary 14E07, 14E30, 14J45
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Sh. Mori, Yu. G. Prokhorov, “Trekhmernye ekstremalnye okrestnosti krivoi s odnoi negorenshteinovoi tochkoi”, Izv. RAN. Ser. matem., 83:3 (2019), 158–212  mathnet  crossref
  • Успехи математических наук Russian Mathematical Surveys
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