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Izv. Akad. Nauk SSSR Ser. Mat., 1970, Volume 34, Issue 4, Pages 778–802 (Mi izv2447)  

This article is cited in 12 scientific papers (total in 12 papers)

On affine surfaces that can be completed by a nonsingular rational curve

M. Kh. Gizatullin


Abstract: It is proved that an affine nonsingular surface which can be completed by a nonsingular rational curve is quasi-homogeneous. The homogeneity of such surfaces is proved in the case of characteristic zero.

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English version:
Mathematics of the USSR-Izvestiya, 1970, 4:4, 787–810

Bibliographic databases:

UDC: 513.6
MSC: 14H45, 14H37, 14J50, 14J17
Received: 19.02.1970

Citation: M. Kh. Gizatullin, “On affine surfaces that can be completed by a nonsingular rational curve”, Izv. Akad. Nauk SSSR Ser. Mat., 34:4 (1970), 778–802; Math. USSR-Izv., 4:4 (1970), 787–810

Citation in format AMSBIB
\Bibitem{Giz70}
\by M.~Kh.~Gizatullin
\paper On affine surfaces that can be completed by a nonsingular rational
curve
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1970
\vol 34
\issue 4
\pages 778--802
\mathnet{http://mi.mathnet.ru/izv2447}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=280491}
\zmath{https://zbmath.org/?q=an:0201.23503|0219.14023}
\transl
\jour Math. USSR-Izv.
\yr 1970
\vol 4
\issue 4
\pages 787--810
\crossref{https://doi.org/10.1070/IM1970v004n04ABEH000933}


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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. M. Kh. Gizatullin, “Invariants of incomplete algebraic surfaces obtained by completions”, Math. USSR-Izv., 5:3 (1971), 503–515  mathnet  crossref  mathscinet  zmath
    2. M. Kh. Gizatullin, “Affine surfaces which are quasihomogeneous with respect to an algebraic group”, Math. USSR-Izv., 5:4 (1971), 754–769  mathnet  crossref  mathscinet  zmath
    3. M. Kh. Gizatullin, “Quasihomogeneous affine surfaces”, Math. USSR-Izv., 5:5 (1971), 1057–1081  mathnet  crossref  mathscinet  zmath
    4. I. V. Dolgachev, “On special algebraic K3 surfaces. I”, Math. USSR-Izv., 7:4 (1973), 833–846  mathnet  crossref  mathscinet  zmath
    5. M. Kh. Gizatullin, V. I. Danilov, “Examples of nonhomogeneous quasihomogeneous surfaces”, Math. USSR-Izv., 8:1 (1974), 43–60  mathnet  crossref  mathscinet  zmath
    6. M. Kh. Gizatullin, V. I. Danilov, “Automorphisms of affine surfaces. II”, Math. USSR-Izv., 11:1 (1977), 51–98  mathnet  crossref  mathscinet  zmath
    7. N. Mohan Kumar, “Rational double points on a rational surface”, Invent math, 65:2 (1981), 251  crossref  mathscinet  zmath  isi
    8. Masayoshi Miyanishi, “Singularities of normal affine surfaces containing cylinderlike open sets”, Journal of Algebra, 68:2 (1981), 268  crossref
    9. Masayoshi Miyanishi, “Affine pseudo-coverings of algebraic surfaces”, Journal of Algebra, 294:1 (2005), 156  crossref
    10. 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
    11. Daniel Daigle, Alejandro Melle-Hernández, “Linear systems of rational curves on rational surfaces”, Mosc. Math. J., 12:2 (2012), 261–268  mathnet  mathscinet
    12. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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