Izvestiya. Mathematics, Tome 18 (1982) no. 3, pp. 537-559
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A. V. Loboda. On local automorphisms of real analytic hypersurfaces. Izvestiya. Mathematics, Tome 18 (1982) no. 3, pp. 537-559. http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a6/
@article{IM2_1982_18_3_a6,
author = {A. V. Loboda},
title = {On local automorphisms of real analytic hypersurfaces},
journal = {Izvestiya. Mathematics},
pages = {537--559},
year = {1982},
volume = {18},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a6/}
}
TY - JOUR
AU - A. V. Loboda
TI - On local automorphisms of real analytic hypersurfaces
JO - Izvestiya. Mathematics
PY - 1982
SP - 537
EP - 559
VL - 18
IS - 3
UR - http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a6/
LA - en
ID - IM2_1982_18_3_a6
ER -
%0 Journal Article
%A A. V. Loboda
%T On local automorphisms of real analytic hypersurfaces
%J Izvestiya. Mathematics
%D 1982
%P 537-559
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a6/
%G en
%F IM2_1982_18_3_a6
In this paper the author studies biholomorphic transformations of $\mathbf C^n$ carrying a nondegenerate real analytic surface $M$ into itself and leaving a particular point $\xi\in M$ fixed. The first estimates of the dimensions of such groups of transformations were obtained by V. K. Beloshapka (see Izv. Akad. Nauk SSSR Ser. Mat., 1979, v. 43, No 2, pp. 243–266). In the present paper it is proved that the dimension of such groups for a nonspherical surface $M$ does not exceed $(n-1)^2$. Bibliography: 2 titles.
