Geodesic
On conic bundle structures
Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 355-390.

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This paper determines under which conditions an algebraic variety can be uniquely (up to equivalence) represented in the form of a conic bundle. The results are used to show that many conic bundles over rational varieties are nonrational, and to construct examples of nonrational algebraic threefolds whose three-dimensional integral cohomology group is trivial. Bibliography: 16 titles. 
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V. G. Sarkisov. On conic bundle structures. Izvestiya. Mathematics , Tome 20 (1983) no. 2, pp. 355-390. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a7/

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