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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 5, Pages 1038–1055 (Mi izv2351)  

This article is cited in 5 scientific papers (total in 5 papers)

Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group

V. L. Popov


Abstract: We find all the affine algebraic surfaces that admit a quasitransitive algebraic group of biregular automorphisms (i.e. a group such that the complement of one orbit of the action is either empty or of dimension zero). The ground field is algebraically closed and of characteristic zero.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:5, 1039–1056

Bibliographic databases:

UDC: 519.4
MSC: Primary 14M15; Secondary 20G20, 57E20
Received: 22.12.1972

Citation: V. L. Popov, “Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group”, Izv. Akad. Nauk SSSR Ser. Mat., 37:5 (1973), 1038–1055; Math. USSR-Izv., 7:5 (1973), 1039–1056

Citation in format AMSBIB
\Bibitem{Pop73}
\by V.~L.~Popov
\paper Classification of affine algebraic surfaces that are quasihomogeneous with respect to an algebraic group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 5
\pages 1038--1055
\mathnet{http://mi.mathnet.ru/izv2351}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=332808}
\zmath{https://zbmath.org/?q=an:0258.14017}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 5
\pages 1039--1056
\crossref{https://doi.org/10.1070/IM1973v007n05ABEH001990}


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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. 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. Kishimoto T., Prokhorov Yu., Zaidenberg M., “Group Actions on Affine Cones”, Affine Algebraic Geometry: the Russell Festschrift, CRM Proceedings & Lecture Notes, 54, eds. Daigle D., Ganong R., Koras M., Amer Mathematical Soc, 2011, 123–163  isi
    4. I. Arzhantsev, M. G. Zaidenberg, K. G. Kuyumzhiyan, “Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity”, Sb. Math., 203:7 (2012), 923–949  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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