V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group $SL(2)$”, Math. USSR-Izv., 7:4 (1973), 793

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Mathematics of the USSR-Izvestiya, 1973, Volume 7, Issue 4, Pages 793–831
DOI: https://doi.org/10.1070/IM1973v007n04ABEH001976 (Mi im2321)

This article is cited in 32 scientific papers (total in 32 papers)

Quasihomogeneous affine algebraic varieties of the group

S L (2)

$SL(2)$

V. L. Popov

English version PDF (1861 kB) Citations (32) Russian version article

References:

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DOI: https://doi.org/10.1070/IM1973v007n04ABEH001976

Abstract: We classify up to

G

$G$ -isomorphism all normal affine irreducible quasihomogeneous (i.e. containing a dense orbit) varieties of the group

G = S L (2)

$G=SL(2)$ which are defined over an algebraically closed field of characteristic zero.

Received: 01.12.1972

Bibliographic databases:

Document Type: Article

UDC: 519.4

MSC: Primary 14L10; Secondary 20G30

Language: English

Original paper language: Russian

Citation: V. L. Popov, “Quasihomogeneous affine algebraic varieties of the group

S L (2)

$SL(2)$ ”, 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 Math. USSR-Izv.

\yr 1973

\vol 7

\issue 4

\pages 793--831

\mathnet{http://mi.mathnet.ru/eng/im2321}

\crossref{https://doi.org/10.1070/IM1973v007n04ABEH001976}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=340263}

\zmath{https://zbmath.org/?q=an:0281.14022}

Linking options:

https://www.mathnet.ru/eng/im2321

https://doi.org/10.1070/IM1973v007n04ABEH001976

https://www.mathnet.ru/eng/im/v37/i4/p792

This publication is cited in the following 32 articles:

I. Arzhantsev, “Automorphisms of algebraic varieties and infinite transitivity”, St. Petersburg Math. J., 34:2 (2023), 143–178
Gene Freudenburg, “Actions of SL2(k) on Affine k-Domains and Fundamental Pairs”, Transformation Groups, 2022
ANDRIY REGETA, “CHARACTERIZATION OF n-DIMENSIONAL NORMAL AFFINE SLn-VARIETIES”, Transformation Groups, 27:1 (2022), 271
AYAKO KUBOTA, “INVARIANT HILBERT SCHEME RESOLUTION OF POPOV'S SL(2)-VARIETIES”, Transformation Groups, 26:4 (2021), 1365
Ayako Kubota, “On minimality of the invariant Hilbert scheme associated to Popov's $\mathit{SL}(2)$ -variety”, Proc. Japan Acad. Ser. A Math. Sci., 96:7 (2020)
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
Alejandro Cabrera, M. Gualtieri, E. Meinrenken, “Dirac Geometry of the Holonomy Fibration”, Commun. Math. Phys., 355:3 (2017), 865
Langlois K. Terpereau R., “on the Geometry of Normal Horospherical G-Varieties of Complexity One”, J. Lie Theory, 26:1 (2016), 49–78
Ivan Arzhantsev, Hubert Flenner, Shulim Kaliman, Frank Kutzschebauch, Mikhail Zaidenberg, Birational Geometry, Rational Curves, and Arithmetic, 2013, 1
I. Arzhantsev, H. Flenner, S. Kaliman, F. Kutzschebauch, M. Zaidenberg, “Flexible varieties and automorphism groups”, Duke Math. J., 162:4 (2013)
Arzhantsev I. Liendo A., “Polyhedral Divisors and Sl2-Actions on Affine T-Varieties”, Mich. Math. J., 61:4 (2012), 731–762
Ivan Arzhantsev, Alvaro Liendo, “Polyhedral divisors and SL2-actions on affine T-varieties”, Michigan Math. J., 61:4 (2012)
S. A. Gaifullin, “Affine toric $\operatorname{SL}(2)$ -embeddings”, Sb. Math., 199:3 (2008), 319–339
V. Batyrev, F. Haddad, “On the Geometry of $\operatorname{SL}(2)$ -Equivariant Flips”, Mosc. Math. J., 8:4 (2008), 621–646
I. V. Arzhantsev, “Contractions of affine spherical varieties”, Sb. Math., 190:7 (1999), 937–954
D. A. Timashev, “Classification of $G$ -varieties of complexity 1”, Izv. Math., 61:2 (1997), 363–397
I. V. Arzhantsev, “On $\operatorname{SL}_2$ -actions of complexity one”, Izv. Math., 61:4 (1997), 685–698
I. V. Arzhantsev, “On actions of reductive groups with one-parameter family”, Sb. Math., 188:5 (1997), 639–655
Franz Pauer, “Closures of SL(2)-orbits in projective spaces”, manuscripta math, 87:1 (1995), 295
D. I. Panyushev, “The canonical module of a quasihomogeneous normal affine $SL_2$ -variety”, Math. USSR-Sb., 73:2 (1992), 569–578

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	532
Russian version PDF:	184
English version PDF:	33
References:	67
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