Geodesic
On the dimension of the group of automorphisms of an analytic hypersurface
Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 223-245

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Let $M$ be a nondegenerate real analytic hypersurface in $\mathbf C^2$, let $\xi\in M$, and let $G_\xi$ consist of the automorphisms of $M$ fixing the point $\xi$. Then, as follows from a theorem of Moser, the real dimension of $G_\xi$ does not exceed 5. Here it is shown that 1) dimensions 2, 3, and 4 cannot be realized, but for 0, 1, and 5 examples are given; 2) if the point $\xi$ is not umbilical, then $G_\xi$ consists of not more than two mappings. Bibliography: 4 titles. 
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     author = {V. K. Beloshapka},
     title = {On the dimension of the group of automorphisms of an analytic hypersurface},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {1980},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a0/}
}
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V. K. Beloshapka. On the dimension of the group of automorphisms of an analytic hypersurface. Izvestiya. Mathematics , Tome 14 (1980) no. 2, pp. 223-245. http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a0/