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Representation of the group of holomorphic symmetries of a real germ in the symmetry group of its model surface. (English. Russian original) Zbl 1146.32018
Math. Notes 82, No. 4, 461-463 (2007); translation from Mat. Zametki 82, No. 4, 515-518 (2007).
Summary: Local polynomial models of real submanifolds of complex spaces were constructed and studied in a series of papers. Among the main features of model surfaces, there is the property that the dimension of the local group of holomorphic symmetries of a germ does not exceed that of the same group of the tangent model surface of this germ.
In the paper, this assertion is rendered much stronger; namely, it is proved that the connected component of the identity element in the symmetry group of a nondegenerate germ is isomorphic as a Lie group to a subgroup of the symmetry group of its tangent model surface.

32V40 Real submanifolds in complex manifolds
32B10 Germs of analytic sets, local parametrization
17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras
Full Text: DOI
[1] V. K. Beloshapka, ”Real submanifolds of a complex space: Their polynomial models, automorphisms, and classification problems.” Usp. Mat. Nauk 57(1), 3–44 (2002) [Russian Math. Surveys 57 (1), 1–41 (2002)]. · Zbl 1053.32022
[2] V. K. Beloshapka, ”A universal model for a real submanifold,” Mat. Zametki 75(4), 507–522 (2004) [Math. Notes 75 (3–4), 475–488 (2004)].
[3] M. S. Baouendi, L. P. Rothschild, J. Winkelmann, and D. Zaitsev, ”Lie group structures of diffeomorphisms and applications to CR manifolds,” Ann. Inst. Fourier (Grenoble) 54, 1279–1303 (2004). · Zbl 1062.22046
[4] A. G. Vitushkin, ”Holomorphic mappings and the geometry of surfaces,” Itogi Nauki Tekh., Ser.: Sovr. Probl. Mat. Fundam. Napravleniya 7, 167–226 (1985) · Zbl 0781.32013
[5] R. V. Gammel’ and I. G. Kossovskii, ”The envelope of holomorphy of a model third-degree surface and the ’rigidity’ phenomenon,” in Trudy Mat. Inst. Steklov (Nauka, Moscow, 2006), Vol. 253, pp. 30–45 [Proc. Steklov Inst. Math., Vol. 253, pp. 22–36 (2006)]. · Zbl 1351.32059
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