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This article is cited in 24 scientific papers (total in 24 papers)
On the dimension of the group of automorphisms of an analytic hypersurface
V. K. Beloshapka
Abstract:
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.
Received: 20.11.1978
Citation:
V. K. Beloshapka, “On the dimension of the group of automorphisms of an analytic hypersurface”, Izv. Akad. Nauk SSSR Ser. Mat., 43:2 (1979), 243–266; Math. USSR-Izv., 14:2 (1980), 223–245
Linking options:
https://www.mathnet.ru/eng/im1681https://doi.org/10.1070/IM1980v014n02ABEH001092 https://www.mathnet.ru/eng/im/v43/i2/p243
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Abstract page: | 376 | Russian version PDF: | 148 | English version PDF: | 7 | References: | 34 | First page: | 1 |
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