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 Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 3, Pages 566–609 (Mi izv2042)

Classification of three-dimensional affine algebraic varieties that are quasi-homogeneous with respect to an algebraic group

V. L. Popov

Abstract: In this article, we find all irreducible three-dimensional affine algebraic varieties that admit a quasi-transitive algebraic group of biregular automorphisms (that is, there is an orbit under the group action whose complement has dimension at most zero). The ground field is algebraically closed and has characteristic zero.
Bibliography: 29 items.

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English version:
Mathematics of the USSR-Izvestiya, 1975, 9:3, 535–576

Bibliographic databases:

UDC: 519.4
MSC: Primary 14J10; Secondary 14L10, 20G20, 20G05, 57A10

Citation: V. L. Popov, “Classification of three-dimensional affine algebraic varieties that are quasi-homogeneous with respect to an algebraic group”, Izv. Akad. Nauk SSSR Ser. Mat., 39:3 (1975), 566–609; Math. USSR-Izv., 9:3 (1975), 535–576

Citation in format AMSBIB
\Bibitem{Pop75} \by V.~L.~Popov \paper Classification of three-dimensional affine algebraic varieties that are quasi-homogeneous with respect to an algebraic group \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1975 \vol 39 \issue 3 \pages 566--609 \mathnet{http://mi.mathnet.ru/izv2042} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=376702} \zmath{https://zbmath.org/?q=an:0308.14009} \transl \jour Math. USSR-Izv. \yr 1975 \vol 9 \issue 3 \pages 535--576 \crossref{https://doi.org/10.1070/IM1975v009n03ABEH001490} 

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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. D. N. Akhiezer, “Dense orbits with two ends”, Math. USSR-Izv., 11:2 (1977), 293–307
2. D. I. Panyushev, “Semisimple automorphism groups of four-dimensional affine space”, Math. USSR-Izv., 23:1 (1984), 171–183
3. Hanspeter Kraft, Vladimir L. Popov, “Semisimple group actions on the three dimensional affine space are linear”, Comment Math Helv, 60:1 (1985), 466
4. V. L. Popov, “Closed orbits of Borel subgroups”, Math. USSR-Sb., 63:2 (1989), 375–392
5. V. L. Popov, “On polynomial automorphisms of affine spaces”, Izv. Math., 65:3 (2001), 569–587
6. 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
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