Real submanifolds in complex space: polynomial models, automorphisms, and classification problems

This is a survey of results on the local theory of real submanifolds of a complex space. Most of the results included here were obtained in Vitushkin's seminar at Moscow State University over the last fifteen years. The most important achievement is a technique for computing automorphisms, invariants, and classifications of real submanifolds, which includes as a main step the construction of a “good” model surface (an analogue of an osculating paraboloid in classical differential geometry).