Projection on Segre varieties and determination of holomorphic mappings between real submanifolds

Details Projection on Segre varieties and determination of holomorphic mappings between real submanifolds Projection on Segre varieties and determination of holomorphic mappings between real submanifolds

2006-09-25

arxiv.org/abs/math/0609677v1

Mathematics

Complex Variables

16 pages

Scientific paper

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.

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