On local automorphisms of real analytic hypersurfaces

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, № 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 $(n-1)^2$.
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