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Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 3, Pages 523–565 (Mi izv2041)  

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

Automorphisms of affine surfaces. I

M. Kh. Gizatullin, V. I. Danilov

Abstract: We study the group of automorphisms $\operatorname{Aut}(X)$ of an affine surface $X$ which can be made complete by adding a zigzag. This study is based on the computation of the action of $\operatorname{Aut}(X)$ on a certain tree $\Delta_X$ associated with the surface $X$. Our results are used to give a description of forms of the surface $X$ and of algebraic subgroups of $\operatorname{Aut}(X)$.
Bibliography: 15 items.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:3, 493–534

Bibliographic databases:

UDC: 513.6
MSC: 14J25
Received: 29.05.1974

Citation: M. Kh. Gizatullin, V. I. Danilov, “Automorphisms of affine surfaces. I”, Izv. Akad. Nauk SSSR Ser. Mat., 39:3 (1975), 523–565; Math. USSR-Izv., 9:3 (1975), 493–534

Citation in format AMSBIB
\by M.~Kh.~Gizatullin, V.~I.~Danilov
\paper Automorphisms of affine surfaces.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 3
\pages 523--565
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 493--534

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    This publication is cited in the following articles:
    1. V. L. Popov, “Classification of three-dimensional affine algebraic varieties that are quasi-homogeneous with respect to an algebraic group”, Math. USSR-Izv., 9:3 (1975), 535–576  mathnet  crossref  mathscinet  zmath
    2. M. Kh. Gizatullin, V. I. Danilov, “Automorphisms of affine surfaces. II”, Math. USSR-Izv., 11:1 (1977), 51–98  mathnet  crossref  mathscinet  zmath
    3. I. R. Shafarevich, “On some infinite-dimensional groups. II”, Math. USSR-Izv., 18:1 (1982), 185–194  mathnet  crossref  mathscinet  zmath
    4. Flenner H., Zaidenberg M., “On the uniqueness of C*-actions on affine surfaces”, Affine Algebraic Geometry, Contemporary Mathematics Series, 369, 2005, 97–111  crossref  isi
    5. Kaliman Sh., “Actions of C* and C+ on affine algebraic varieties”, Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, 80, no. 1- 2, 2009, 629–654  isi
    6. Yu. M. Polyakova, “A family of categories of log terminal pairs and automorphisms of surfaces”, Izv. Math., 74:3 (2010), 541–593  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Kishimoto T. Prokhorov Yu. Zaidenberg M., “Group Actions on Affine Cones”, Affine Algebraic Geometry: the Russell Festschrift, CRM Proceedings & Lecture Notes, 54, ed. Daigle D. Ganong R. Koras M., Amer Mathematical Soc, 2011, 123–163  isi
    8. Arzhantsev I., Zaidenberg M., “Acyclic Curves and Group Actions on Affine Toric Surfaces”, Affine Algebraic Geometry, eds. Masuda K., Kojima H., Kishimoto T., World Scientific Publ Co Pte Ltd, 2013, 1–41  isi
    9. Dubouloz A. Lamy S., “Automorphisms of Open Surfaces With Irreducible Boundary”, Osaka J. Math., 52:3 (2015), 747–791  isi
    10. Kovalenko S. Perepechko A. Zaidenberg M., “On Automorphism Groups of Affine Surfaces”, Algebraic Varieties and Automorphism Groups, Advanced Studies in Pure Mathematics, 75, ed. Masuda K. Kishimoto T. Kojima H. Miyanishi M. Zaidenberg M., Math Soc Japan, 2017, 207–286  isi
    11. Dubouloz A., Mangolte F., “Fake Real Planes: Exotic Affine Algebraic Models of R-2”, Sel. Math.-New Ser., 23:3 (2017), 1619–1668  crossref  isi
    12. A. V. Pukhlikov, “Automorphisms of certain affine complements in projective space”, Sb. Math., 209:2 (2018), 276–289  mathnet  crossref  crossref  adsnasa  isi  elib
    13. Cheltsov I. Dubouloz A. Park J., “Super-Rigid Affine Fano Varieties”, Compos. Math., 154:11 (2018), 2462–2484  crossref  mathscinet  zmath  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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