Projection on Segre varieties and determination of holomorphic mappings between real submanifolds
arXiv:math/0609677 · doi:10.1007/s11425-006-2067-4
Abstract
It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is given for a germ of a mapping into the Segre variety of the target manifold to be the projection of a holomorphic mapping sending the source manifold into the target. An application to the biholomorphic equivalence problem is also given.
16 pages