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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 3–20 (Mi izv344)  

This article is cited in 7 scientific papers (total in 7 papers)

Polynomial models of real manifolds

V. K. Beloshapka

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We construct polynomial models for germs of real submanifolds in complex space. It was shown earlier that the properties of models of degree 3 (for appropriate values of the codimension) are similar to well-known properties of tangent quadrics. In this paper we construct models of arbitrarily high degree. They have all these properties with one exception: from degree 5 onwards, they are not completely universal.

DOI: https://doi.org/10.4213/im344

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English version:
Izvestiya: Mathematics, 2001, 65:4, 641–657

Bibliographic databases:

MSC: 32V99
Received: 13.02.2001

Citation: V. K. Beloshapka, “Polynomial models of real manifolds”, Izv. RAN. Ser. Mat., 65:4 (2001), 3–20; Izv. Math., 65:4 (2001), 641–657

Citation in format AMSBIB
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\by V.~K.~Beloshapka
\paper Polynomial models of real manifolds
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 3--20
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\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 641--657
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000344}
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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. K. Beloshapka, “Real submanifolds in complex space: polynomial models, automorphisms, and classification problems”, Russian Math. Surveys, 57:1 (2002), 1–41  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. K. Beloshapka, “Universal Models For Real Submanifolds”, Math. Notes, 75:4 (2004), 475–488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. E. N. Shananina, “Polynomial Models of Degree 5 and Algebras of Their Automorphisms”, Math. Notes, 75:5 (2004), 702–716  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. G. Kossovskii, “On envelopes of holomorphy of model manifolds”, Izv. Math., 71:3 (2007), 545–571  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Wu Q., “On holomorphic automorphisms of a class of non-homogeneous rigid hypersurfaces in a", (N+1)”, Chinese Annals of Mathematics Series B, 31:2 (2010), 201–210  crossref  mathscinet  zmath  isi  scopus
    6. V. K. Beloshapka, “Model-surface method: An infinite-dimensional version”, Proc. Steklov Inst. Math., 279 (2012), 14–24  mathnet  crossref  mathscinet  isi
    7. Sabzevari M., Hashemi A., Alizadeh B.M., Merker J., “Lie algebras of infinitesimal CR automorphisms of weighted homogeneous and homogeneous CR-generic submanifolds of CN”, Filomat, 30:6 (2016), 1387–1411  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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