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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 4, Pages 918–945 (Mi izv1862)  

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)
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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
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\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
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\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}
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    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:
    1. V. G. Sarkisov, “On conic bundle structures”, Math. USSR-Izv., 20:2 (1983), 355–390  mathnet  crossref  mathscinet  zmath
    2. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. A. Iskovskikh, “On the rationality problem for conic bundles”, Math. USSR-Sb., 72:1 (1992), 105–111  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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+  mathscinet  isi
    5. V. A. Iskovskikh, “A rationality criterion for conic bundles”, Sb. Math., 187:7 (1996), 1021–1038  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. A. V. Pukhlikov, “Birational automorphisms of algebraic threefolds with a pencil of Del Pezzo surfaces”, Izv. Math., 62:1 (1998), 115–155  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. M. M. Grinenko, “On Fibrations into del Pezzo Surfaces”, Math. Notes, 69:4 (2001), 499–513  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. S. Boukraa, S. Hassani, J.-M. Maillard, “Noetherian mappings”, Physica D: Nonlinear Phenomena, 185:1 (2003), 3  crossref
    10. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 196:1 (2005), 77–114  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Aleksandr V. Pukhlikov, “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, manuscripta math, 121:4 (2006), 491  crossref  mathscinet  zmath  isi  elib
    17. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Cheltsov I., “Nonrational nodal quartic threefolds”, Pacific Journal of Mathematics, 226:1 (2006), 65–81  crossref  isi  elib
    20. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    21. I. A. Cheltsov, K. A. Shramov, “Log canonical thresholds of smooth Fano threefolds”, Russian Math. Surveys, 63:5 (2008), 859–958  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    22. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. Pukhlikov, AV, “Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers”, Pure and Applied Mathematics Quarterly, 5:2 (2009), 641  isi  elib
    24. Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011  crossref
    25. Ahmadinezhad H., “On Del Pezzo Fibrations That Are Not Birationally Rigid”, J. Lond. Math. Soc.-Second Ser., 86:Part 1 (2012), 36–62  crossref  isi
    26. Marcello Bernardara, Michele Bolognesi, “Derived categories and rationality of conic bundles”, Compositio Math, 2013, 1  crossref
    27. 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  crossref
    28. Michela Brundu, Gianni Sacchiero, “On the Singularities of Surfaces Ruled by Conics”, Communications in Algebra, 42:5 (2014), 1857  crossref
    29. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. Kollar J., “Conic Bundles That Are Not Birational to Numerical Calabi-Yau Pairs”, Epijournal Geom. Algebr., 1 (2017), UNSP 1  isi
    32. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
    33. Cheltsov I. Przyjalkowski V. Shramov C., “Which Quartic Double Solids Are Rational?”, J. Algebr. Geom., 28:2 (2019), 201–243  crossref  mathscinet  zmath  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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