V. A. Iskovskikh, “A rationality criterion for conic bundles”, Sb. Math., 187:7 (1996), 1021

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Sbornik: Mathematics, 1996, Volume 187, Issue 7, Pages 1021–1038
DOI: https://doi.org/10.1070/SM1996v187n07ABEH000145 (Mi sm145)

This article is cited in 22 scientific papers (total in 23 papers)

A rationality criterion for conic bundles

V. A. Iskovskikh

English version PDF (877 kB) Citations (23) Russian version article

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DOI: https://doi.org/10.1070/SM1996v187n07ABEH000145

Abstract: 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

$p_a(C)>18$ .

Received: 25.01.1996

Bibliographic databases:

Document Type: Article

UDC: 512.6

MSC: Primary 14J30; Secondary 14E35, 14K30, 14E05, 14J17, 14J26

Language: English

Original paper language: Russian

Citation: V. A. Iskovskikh, “A rationality criterion for conic bundles”, Sb. Math., 187:7 (1996), 1021–1038

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm145

https://doi.org/10.1070/SM1996v187n07ABEH000145

https://www.mathnet.ru/eng/sm/v187/i7/p75

This publication is cited in the following 23 articles:

Corti A. Gugiatti G., “Hyperelliptic Integrals and Mirrors of the Johnson-Kollar Del Pezzo Surfaces”, Trans. Am. Math. Soc., 374:12 (2021), 8603–8637
Sh. Mori, Yu. G. Prokhorov, “Threefold extremal curve germs with one non-Gorenstein point”, Izv. Math., 83:3 (2019), 565–612
Ahmadinezhad H., Okada T., “Stable Rationality of Higher Dimensional Conic Bundles”, Epijournal Geom. Algebr., 2 (2018), UNSP 5
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
Michela Brundu, Gianni Sacchiero, “On the Singularities of Surfaces Ruled by Conics”, Communications in Algebra, 42:5 (2014), 1857
Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011
Katzarkov L., “Homological Mirror Symmetry and Algebraic Cycles”, Riemannian Topology and Geometric Structures on Manifolds, Progress in Mathematics, 271, 2009, 63–92
Katzarkov L., “Homological Mirror Symmetry and Algebraic Cycles”, Homological Mirror Symmetry: New Developments and Perspectives, Lecture Notes in Physics, 757, 2009, 125–152
Mori, S, “On Q-conic bundles”, Publications of the Research Institute For Mathematical Sciences, 44:2 (2008), 315
M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300
Ivan Cheltsov, “Nonrational nodal quartic threefolds”, Pacific J Math, 226:1 (2006), 65
I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965
V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421
I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071
Lin, JY, “Birational unboundedness of Q-Fano threefolds”, International Mathematics Research Notices, 2003, no. 6, 301
V. A. Iskovskikh, “Birational rigidity of Fano hypersurfaces in the framework of Mori theory”, Russian Math. Surveys, 56:2 (2001), 207–291
Prokhorov, YG, “Boundedness of nonbirational extremal contractions”, International Journal of Mathematics, 11:3 (2000), 393
A. I. Kostrikin, V. S. Kulikov, Yu. I. Manin, V. V. Nikulin, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, A. N. Tyurin, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (on his 60th birthday)”, Russian Math. Surveys, 54:4 (1999), 863–868
Yu. G. Prokhorov, “On extremal contractions from threefolds to surfaces: The case of one non-Gorenstein point and a nonsingular base surface”, J Math Sci, 95:1 (1999), 1986

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	573
Russian version PDF:	266
English version PDF:	80
References:	62
First page:	4

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