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On conic bundle structures. (Russian. English original) Zbl 0593.14034
Math. USSR, Izv. 20, 355-390 (1983); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 46, No. 2, 371-408 (1982).
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.

MSC:
14M20 Rational and unirational varieties
14E05 Rational and birational maps
14J30 \(3\)-folds
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