On dimensions of the groups of biholomorphic automorphisms of real-analytic hypersurfaces

In this paper we study the dependence of the local geometry of real-analytic hypersurfaces in $\mathbb C^n$ on the dimension of the group of biholomorphic automorphisms of this surface. We also classify the hypersurfaces in terms of this group. We present some examples showing that the classes of the given construction are not empty. We find a new formulation of the Freeman theorem on the so-called straightening of a real-analytic $\operatorname{CR}$-submanifold in $\mathbb C^n$ with degenerate Levi form of constant rank.