Geodesic
A rationality criterion for conic bundles
Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 1021-1038 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is that a three-dimensional variety $X$ that is a conic bundle $\pi\colon X\to S$ in the Mori sense has a base with at most double rational singularities of type $A_n$. A rationality criterion is proved subject to this assumption in the case when the discriminant curve $C\subset S$ is large enough, for example, for the case when $p_a(C)>18$. 
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     author = {V. A. Iskovskikh},
     title = {A rationality criterion for conic bundles},
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     url = {http://geodesic.mathdoc.fr/item/SM_1996_187_7_a3/}
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V. A. Iskovskikh. A rationality criterion for conic bundles. Sbornik. Mathematics, Tome 187 (1996) no. 7, pp. 1021-1038. http://geodesic.mathdoc.fr/item/SM_1996_187_7_a3/

[1] Alekseev V. A., “Usloviya ratsionalnosti trekhmernykh mnogoobrazii s puchkom poverkhnostei Del Petstso stepeni 4”, Matem. zametki, 41:5 (1987), 724–730 | MR

[2] Alekseev V. A., Nikulin V. V., “Klassifikatsiya poverkhnostei Del Petstso s log-terminalnymi osobennostyami indeksa 2, involyutsii na poverkhnostyakh K3 i gruppy otrazhenii v prostranstvakh Lobachevskogo”, Doklady po matematike i ee prilozheniyam, 2, no. 2, Izd-vo Moskva–Tula, 1988, 51–150 | MR

[3] Beltrametti M., “On the Chow group and the intermediate Jacobian of conic bundle”, Ann. Mat. Pura Appl. (4), 141 (1985), 331–351 | DOI | MR | Zbl

[4] Bindschadler D., Brenton L., Drucker D., “Rational mappings of Del Pezzo surfaces, and singular compactifications of two-dimensional affine varieties”, Tôhoku Math. J., 36:4 (1984), 519–609 | DOI | MR

[5] Beauville A., “Varieties de Prym et Jacobiennes intermediares”, Ann. Sci. École Norm. Sup. (4), 10:3 (1977), 309–399 | MR

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

[7] Cutkosky S., “Elementary contractions of Gorenstein threefolds”, Math. Ann., 280 (1988), 521–525 | DOI | MR | Zbl

[8] Iskovskikh V. A., “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh i s polozhitelnym kvadratom kanonicheskogo klassa”, Matem. sb., 83(125):1 (1970), 90–119 | MR | Zbl

[9] Iskovskikh V. A., “K probleme ratsionalnykh rassloenii na koniki”, Matem. sb., 182:1 (1991), 114–121 | MR

[10] Iskovskikh V. A., “On the rationality problem for conic bundlese”, Duke Math. J., 54:2 (1987), 271–294 | DOI | MR | Zbl

[11] Kanev V. I., Katsarkov L. V., “Universal properties of Prym varieties of singular curves”, C. R. Acad. Bulgare Sci., 41:10 (1988), 25–27 | MR | Zbl

[12] Kollar J., Miyaoka Y., Mori S., “Rational connected varieties”, J. Algebraic Geom., 1 (1992), 429–448 | MR | Zbl

[13] Miyanishi M., “Algebraic varieties and Analytic varieties”, Adv. Stud. Pure Math., 71 (1983), 69–99 | MR

[14] Prokhorov Yu., On the $\mathbb Q$-Fano fiber spaces with two-dimensional base, Preprint MPI 95/33, 1995 | MR

[15] Prokhorov Yu., On extremal contractions from threefolds to surfaces, Preprint of Univ. Warwick, 1995 | MR

[16] Sarkisov V. G., “Biratsionalnye avtomorfizmy rassloenii na koniki”, Izv. AN SSSR. Ser. matem., 44:4 (1980), 918–945 | MR | Zbl

[17] Shokurov V. V., “Mnogoobraziya Prima: teoriya i prilozheniya”, Izv. AN SSSR. Ser. matem., 47:4 (1983), 785–855 | MR