Dynamics of the Segre varieties of a real submanifold in complex space

Details Dynamics of the Segre varieties of a real submanifold in complex space Dynamics of the Segre varieties of a real submanifold in complex space

2000-08-15

arxiv.org/abs/math/0008112v1

Mathematics

Complex Variables

23 pages, LaTeX 2e

Scientific paper

Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre mappings for smooth or formal submanifolds. In particular, we characterize finite type in terms of the rank of the iterated Segre mappings. The approach given here is new, simplifies proofs, and extends results previously known for the real analytic case.

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