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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 4, Pages 792–832 (Mi izv2321)  

This article is cited in 18 scientific papers (total in 18 papers)

Quasihomogeneous affine algebraic varieties of the group $SL(2)$

V. L. Popov


Abstract: We classify up to $G$-isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group $G=SL(2)$ which are defined over an algebraically closed field of characteristic zero.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:4, 793–831

Bibliographic databases:

UDC: 519.4
MSC: Primary 14L10; Secondary 20G30
Received: 01.12.1972

Citation: V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group $SL(2)$”, Izv. Akad. Nauk SSSR Ser. Mat., 37:4 (1973), 792–832; Math. USSR-Izv., 7:4 (1973), 793–831

Citation in format AMSBIB
\Bibitem{Pop73}
\by V.~L.~Popov
\paper Quasihomogeneous affine algebraic varieties of the group~$SL(2)$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 4
\pages 792--832
\mathnet{http://mi.mathnet.ru/izv2321}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=340263}
\zmath{https://zbmath.org/?q=an:0281.14022}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 4
\pages 793--831
\crossref{https://doi.org/10.1070/IM1973v007n04ABEH001976}


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    Citing articles on Google Scholar: Russian citations, English citations
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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. Hanspeter Kraft, Claudio Procesi, “On the geometry of conjugacy classes in classical groups”, Comment Math Helv, 57:1 (1982), 539  crossref  mathscinet  zmath  isi
    3. Franz Pauer, “Glatte Einbettungen vonG/U”, Math Ann, 262:3 (1983), 421  crossref  mathscinet  zmath  isi
    4. V. L. Popov, “Syzygies in the theory of invariants”, Math. USSR-Izv., 22:3 (1984), 507–585  mathnet  crossref  mathscinet  zmath
    5. V. L. Popov, “Contractions of the actions of reductive algebraic groups”, Math. USSR-Sb., 58:2 (1987), 311–335  mathnet  crossref  mathscinet  zmath
    6. D. I. Panyushev, “The structure of the canonical module and the Gorenstein property for some quasihomogeneous varieties”, Math. USSR-Sb., 65:1 (1990), 81–95  mathnet  crossref  mathscinet  zmath
    7. D. I. Panyushev, “Resolution of singularities of affine normal quasihomogeneous $SL_2$-varieties”, Funct. Anal. Appl., 22:4 (1988), 338–339  mathnet  crossref  mathscinet  zmath  isi
    8. D. I. Panyushev, “The canonical module of a quasihomogeneous normal affine $SL_2$-variety”, Math. USSR-Sb., 73:2 (1992), 569–578  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. Franz Pauer, “Closures of SL(2)-orbits in projective spaces”, manuscripta math, 87:1 (1995), 295  crossref  mathscinet  zmath  isi
    10. D. A. Timashev, “Classification of $G$-varieties of complexity 1”, Izv. Math., 61:2 (1997), 363–397  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. I. V. Arzhantsev, “On $\operatorname{SL}_2$-actions of complexity one”, Izv. Math., 61:4 (1997), 685–698  mathnet  crossref  crossref  mathscinet  zmath  isi
    12. I. V. Arzhantsev, “On actions of reductive groups with one-parameter family”, Sb. Math., 188:5 (1997), 639–655  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. I. V. Arzhantsev, “Contractions of affine spherical varieties”, Sb. Math., 190:7 (1999), 937–954  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. S. A. Gaifullin, “Affine toric $\operatorname{SL}(2)$-embeddings”, Sb. Math., 199:3 (2008), 319–339  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$-Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646  mathnet  crossref  mathscinet  zmath
    16. Arzhantsev I. Liendo A., “Polyhedral Divisors and Sl2-Actions on Affine T-Varieties”, Mich. Math. J., 61:4 (2012), 731–762  isi
    17. Langlois K. Terpereau R., “on the Geometry of Normal Horospherical G-Varieties of Complexity One”, J. Lie Theory, 26:1 (2016), 49–78  mathscinet  zmath  isi  elib
    18. 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
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