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Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 110–144 (Mi izv1634)  

This article is cited in 13 scientific papers (total in 13 papers)

Rational $G$-surfaces

M. Kh. Gizatullin

Abstract: In this paper the author determines the structure of complete rational surfaces on which one can define a group action in such a way that for each element of the group there exists a nonzero linear equivalence divisor class with nonnegative self-intersection index which is invariant with respect to this element. If one excludes the case when this action factors through an algebraic action of a linear algebraic group, then all such surfaces are elliptic bundles, and the action of the group preserves the family of fibers.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 103–134

Bibliographic databases:

UDC: 513.6
MSC: Primary 14L30; Secondary 14J25
Received: 20.08.1979

Citation: M. Kh. Gizatullin, “Rational $G$-surfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 110–144; Math. USSR-Izv., 16:1 (1981), 103–134

Citation in format AMSBIB
\by M.~Kh.~Gizatullin
\paper Rational $G$-surfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 110--144
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 103--134

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    This publication is cited in the following articles:
    1. 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
    2. Masanori Koitabashi, “Automorphism groups of generic rational surfaces”, Journal of Algebra, 116:1 (1988), 130  crossref
    3. D.-Q Zhang, “Automorphisms of Finite Order on Rational Surfaces”, Journal of Algebra, 238:2 (2001), 560  crossref
    4. J-Ch Angl s d Auriac, J-M Maillard, C M Viallet, “A classification of four-state spin edge Potts models”, J Phys A Math Gen, 35:44 (2002), 9251  crossref  mathscinet  zmath  adsnasa  elib
    5. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. A. Cheltsov, “Rationality of an Enriques–Fano threefold of genus five”, Izv. Math., 68:3 (2004), 607–618  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. Curtis T. McMullen, “Dynamics on blowups of the projective plane”, Publ math IHES, 105:1 (2007), 49  crossref  mathscinet  zmath  isi
    9. Serge Cantat, Stéphane Lamy, Yves Cornulier, “Normal subgroups in the Cremona group”, Acta Math, 210:1 (2013), 31  crossref
    10. Eric Bedford, Serge Cantat, Kyounghee Kim, “Pseudo-automorphisms with no invariant foliation”, JMD, 8:2 (2014), 221  crossref
    11. Blanc J. Calabri A., “on Degenerations of Plane Cremona Transformations”, Math. Z., 282:1-2 (2016), 223–245  crossref  isi
    12. Julien Grivaux, “Parabolic automorphisms of projective surfaces (after M. H. Gizatullin)”, Mosc. Math. J., 16:2 (2016), 275–298  mathnet  crossref  mathscinet
    13. Cantat S., “The Cremona Group”, Algebraic Geometry: Salt Lake City 2015, Pt 1, Proceedings of Symposia in Pure Mathematics, 97, no. 1, eds. DeFernex T., Hassett B., Mustata M., Olsson M., Popa M., Thomas R., Amer Mathematical Soc, 2018, 101–142  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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