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 Tr. Mat. Inst. Steklova, 2001, Volume 235, Pages 7–35 (Mi tm231)

A Quasiperiodic System of Polynomial Models of CR-Manifolds

V. K. Beloshapka

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

Abstract: Polynomial models for the germs of real submanifolds of a complex space are constructed. For the germs whose Levi–Tanaka algebra has length 2, such a sufficiently well-studied model is given by a tangent quadric. It is shown that models of the third and fourth degrees (algebras of lengths 3 and 4) possess, in their codimension ranges, a full spectrum of properties that are completely analogous to the properties of tangent quadrics. For the constructed higher order models, a full spectrum of properties is obtained with the only exception that they are not fully universal.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 235, 1–28

Bibliographic databases:

UDC: 514.763.47
Received in February 2001

Citation: V. K. Beloshapka, “A Quasiperiodic System of Polynomial Models of CR-Manifolds”, Analytic and geometric issues of complex analysis, Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin, Tr. Mat. Inst. Steklova, 235, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 7–35; Proc. Steklov Inst. Math., 235 (2001), 1–28

Citation in format AMSBIB
\Bibitem{Bel01} \by V.~K.~Beloshapka \paper A~Quasiperiodic System of Polynomial Models of CR-Manifolds \inbook Analytic and geometric issues of complex analysis \bookinfo Collected papers. Dedicated to the 70th anniversary of academician Anatolii Georgievich Vitushkin \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 235 \pages 7--35 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm231} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1886570} \zmath{https://zbmath.org/?q=an:1013.32022} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 235 \pages 1--28 

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This publication is cited in the following articles:
1. V. K. Beloshapka, “Universal Models For Real Submanifolds”, Math. Notes, 75:4 (2004), 475–488
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