Let A be an algebraic variety of codimension at least 2 in C^N. Let E_1={a_j} be a discrete set in C^N\A such that the series with entries 1/|a_j|^2 converges, and let E_2={b_j} be be another such set. Let G be a holomorphic automorphism of C^N which is the identity on A. Let K be a polynomially convex compact set in C^N such that K does no intersect E_1 and G(K) does not intersect E_2. Then there exists a holomorphic automorphism of C^N that is the identity on A, that approximates G on K, and that maps a_j to b_j for all j=1,2,...
COBISS.SI-ID: 15194713
The author gives a detailed analysis of the CR structure of the preimage of a CR submanifold by a generic holomorphic map. In particular, he gave a detailed description of a stratification whose strata have constant CR dimension.
COBISS.SI-ID: 15194457