Geodesic
The rationality problem for conic bundles
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 3, pp. 375-456

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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, intermediate Jacobian, Prym variety.
Mots-clés : invariants, birational transformations, Sarkisov programme 
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     author = {Yu. G. Prokhorov},
     title = {The rationality problem for conic bundles},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     url = {http://geodesic.mathdoc.fr/item/RM_2018_73_3_a0/}
}
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Yu. G. Prokhorov. The rationality problem for conic bundles. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 3, pp. 375-456. http://geodesic.mathdoc.fr/item/RM_2018_73_3_a0/