Representation of the Group of Holomorphic Symmetries of a Real Germ in the Symmetry Group of Its Model Surface

Local polynomial models of real submanifolds of complex space were constructed and studied in a series of papers. Among the main features of model surfaces, there is the property that the dimension of the local group of holomorphic symmetries of a germ does not exceed that of the same group of the tangent model surface of this germ. In the paper, this assertion is rendered much stronger; namely, it is proved that the connected component of the identity element in the symmetry group of a nondegenerate germ is isomorphic as a Lie group to a subgroup of the symmetry group of its tangent model surface.