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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 1, Pages 54–103 (Mi izv1793)  

This article is cited in 11 scientific papers (total in 11 papers)

Automorphisms of affine surfaces. II

M. Kh. Gizatullin, V. I. Danilov


Abstract: Affine surfaces $X$ completed by an irreducible rational curve $C$ are studied. The integer $m=(C^2)$ is an invariant of $X$. It is shown that the set of all such surfaces with fixed invariant $m$ is described in terms of orbits of a group action on the space of “tails”; moreover, the automorphism group $\operatorname{Aut}(X)$ is expressed by the stabilizers of the action. Explicit formulas for generators of the group $\operatorname{Aut}(X)$ are given for $m\leqslant5$. In particular, it is shown that in zero characteristic the invariant $m$ uniquely determines the surface $X$; in the general case this is not so.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1977, 11:1, 51–98

Bibliographic databases:

UDC: 513.6
MSC: Primary 14E05; Secondary 14J25
Received: 17.03.1976

Citation: M. Kh. Gizatullin, V. I. Danilov, “Automorphisms of affine surfaces. II”, Izv. Akad. Nauk SSSR Ser. Mat., 41:1 (1977), 54–103; Math. USSR-Izv., 11:1 (1977), 51–98

Citation in format AMSBIB
\Bibitem{GizDan77}
\by M.~Kh.~Gizatullin, V.~I.~Danilov
\paper Automorphisms of affine surfaces.~II
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 1
\pages 54--103
\mathnet{http://mi.mathnet.ru/izv1793}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=437545}
\zmath{https://zbmath.org/?q=an:0357.14003|0379.14002}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 1
\pages 51--98
\crossref{https://doi.org/10.1070/IM1977v011n01ABEH001695}


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    This publication is cited in the following articles:
    1. Richard Ganong, Peter Russell, “Derivations with only divisorial singularities on rational and ruled surfaces”, Journal of Pure and Applied Algebra, 26:2 (1982), 165  crossref
    2. I. R. Shafarevich, “On the Group $GL(2,K[t])$”, Proc. Steklov Inst. Math., 246 (2004), 308–314  mathnet  mathscinet  zmath
    3. BURT TOTARO, “The automorphism group of an affine quadric”, Math Proc Camb Phil Soc, 143:1 (2007), 1  crossref  mathscinet  zmath  isi
    4. Hubert Flenner, Shulim Kaliman, Mikhail Zaidenberg, “Embeddings of
      $${\mathbb{C}^*}$$
      -surfaces into weighted projective spaces”, manuscripta math, 2009  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. Farkhod Eshmatov, Alimjon Eshmatov, Yuri Berest, “On subgroups of the Dixmier group and Calogero–Moser spaces”, ERA-MS, 18 (2011), 12  crossref
    8. 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
    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, eds. Masuda K., Kishimoto T., Kojima H., Miyanishi M., Zaidenberg M., Math Soc Japan, 2017, 207–286  isi
    11. A. V. Pukhlikov, “Automorphisms of certain affine complements in projective space”, Sb. Math., 209:2 (2018), 276–289  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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