|
This article is cited in 32 scientific papers (total in 33 papers)
Birational automorphisms of conic bundles
V. G. Sarkisov
Abstract:
This paper studies birational automorphisms of algebraic threefolds representable in the form of conic bundles. It is shown that, under certain conditions on the degeneration curve of a conic bundle, the automorphisms preserve the conic bundle structure.
Bibliography: 18 titles.
 Full text:
PDF file (2511 kB)
References:
PDF file
HTML file
English version:
Mathematics of the USSR-Izvestiya, 1981, 17:1, 177–202
Bibliographic databases:
  
UDC:
513.6
MSC: Primary 14E35; Secondary 14J30, 14M20
Received: 11.03.1980
Citation:
V. G. Sarkisov, “Birational automorphisms of conic bundles”, Izv. Akad. Nauk SSSR Ser. Mat., 44:4 (1980), 918–945; Math. USSR-Izv., 17:1 (1981), 177–202
Citation in format AMSBIB
\Bibitem{Sar80}
\by V.~G.~Sarkisov
\paper Birational automorphisms of conic bundles
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 4
\pages 918--945
\mathnet{http://mi.mathnet.ru/izv1862}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=587343}
\zmath{https://zbmath.org/?q=an:0466.14012|0453.14017}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 17
\issue 1
\pages 177--202
\crossref{https://doi.org/10.1070/IM1981v017n01ABEH001326}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MW12300008}
Linking options:
http://mi.mathnet.ru/eng/izv1862 http://mi.mathnet.ru/eng/izv/v44/i4/p918
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
V. G. Sarkisov, “On conic bundle structures”, Math. USSR-Izv., 20:2 (1983), 355–390
 -
Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116
 -
V. A. Iskovskikh, “On the rationality problem for conic bundles”, Math. USSR-Sb., 72:1 (1992), 105–111
-
Kollar J., “Flips and Abundance for Algebraic Threefolds - a Summer Seminar at the University-of-Utah (Salt-Lake-City, 1991) - Preface”, Asterisque, 1992, no. 211, 1+
-
V. A. Iskovskikh, “A rationality criterion for conic bundles”, Sb. Math., 187:7 (1996), 1021–1038
-
A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155
 -
M. M. Grinenko, “On Fibrations into del Pezzo Surfaces”, Math. Notes, 69:4 (2001), 499–513
-
A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596
-
S. Boukraa, S. Hassani, J.-M. Maillard, “Noetherian mappings”, Physica D: Nonlinear Phenomena, 185:1 (2003), 3
-
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071
-
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702
-
I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275
-
A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255
-
Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 196:1 (2005), 77–114
-
I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965
-
Aleksandr V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, manuscripta math, 121:4 (2006), 491
-
A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368
-
M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300
-
Cheltsov I., “Nonrational nodal quartic threefolds”, Pacific Journal of Mathematics, 226:1 (2006), 65–81
-
A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
-
I. A. Cheltsov, K. A. Shramov, “Log canonical thresholds of smooth Fano threefolds”, Russian Math. Surveys, 63:5 (2008), 859–958
-
F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946
-
Pukhlikov, AV, “Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers”, Pure and Applied Mathematics Quarterly, 5:2 (2009), 641
-
Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011
-
Ahmadinezhad H., “On Del Pezzo Fibrations That Are Not Birationally Rigid”, J. Lond. Math. Soc.-Second Ser., 86:Part 1 (2012), 36–62
-
Marcello Bernardara, Michele Bolognesi, “Derived categories and rationality of conic bundles”, Compositio Math, 2013, 1
-
Asher Auel, Marcello Bernardara, Michele Bolognesi, “Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems”, Journal de Mathématiques Pures et Appliquées, 2013
-
Michela Brundu, Gianni Sacchiero, “On the Singularities of Surfaces Ruled by Conics”, Communications in Algebra, 42:5 (2014), 1857
-
A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837
-
A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644
-
Kollar J., “Conic Bundles That Are Not Birational to Numerical Calabi-Yau Pairs”, Epijournal Geom. Algebr., 1 (2017), UNSP 1
-
Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456
-
Cheltsov I. Przyjalkowski V. Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243
|
| Number of views: |
| This page: | 382 | | Full text: | 134 | | References: | 31 | | First page: | 2 |
|
Terms of Use