Geodesic
Conic bundles with big discriminant loci
Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 429-434.

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We prove that conic bundles with sufficiently big discriminant locus cannot be birationally transformed into fibrations whose generic fibre has numerically trivial canonical divisor. 
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I. A. Cheltsov. Conic bundles with big discriminant loci. Izvestiya. Mathematics , Tome 68 (2004) no. 2, pp. 429-434. http://geodesic.mathdoc.fr/item/IM2_2004_68_2_a9/

[1] Sarkisov V. G., “O strukture rassloeniya na koniki”, Izv. AN SSSR. Ser. matem., 46:2 (1982), 371–408 | MR | Zbl

[2] Bogomolov F., Tschinkel Yu., “On the density of rational points on elliptic fibrations”, J. Reine Angew. Math., 511 (1999), 87–93 | MR | Zbl

[3] Harris J., Tschinkel Yu., “Rational points on quartics”, Duke Math. J., 104 (2000), 477–500 | DOI | MR | Zbl

[4] Cheltsov I., “Log pairs on birationally rigid varieties”, J. Math. Sci., 102 (2000), 3843–3875 | DOI | MR | Zbl

[5] Corti A., “Factorizing birational maps of threefolds after Sarkisov”, J. Alg. Geom., 4 (1995), 223–254 | MR | Zbl

[6] Iskovskikh V. A., “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh”, Matem. sb., 74:4 (1967), 608–638 | MR | Zbl

[7] Artin M., Mumford D., “Some elementary examples of unirational varieties which are not rational”, Proc. London Math. Soc., 25 (1972), 75–95 | DOI | MR | Zbl

[8] Zagorskii A. A., “O trekhmernykh rassloeniyakh na koniki”, Matem. zametki, 21 (1977), 745–758 | MR | Zbl

[9] Beauville A., “Variétés de Prym et Jacobiennes intermédiaires”, Ann. Sci. de l'Ecole Norm. Sup., 10 (1977), 304–392 | MR