Equivalences of real submanifolds in complex space

Details Equivalences of real submanifolds in complex space Equivalences of real submanifolds in complex space

2000-02-22

arxiv.org/abs/math/0002186v1

Mathematics

Complex Variables

38 pages, LateX

Scientific paper

We show that for any real-analytic submanifold M in C^N there is a proper real-analytic subvariety V contained in M such that for any point p in M\V, any real-analytic submanifold M' in C^N, and any point p' in M', the germs of the submanifolds M and M' at p and p' respectively are formally equivalent if and only if they are biholomorphically equivalent. More general results for k-equivalences are also stated and proved.

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