Convergence and finite determination of formal CR mappings

Details Convergence and finite determination of formal CR mappings Convergence and finite determination of formal CR mappings

1999-04-16

arxiv.org/abs/math/9904085v1

Mathematics

Complex Variables

AMS-TeX (amsppt); 29 pages

Scientific paper

It is shown that a formal mapping between two real-analytic hypersurfaces in complex space is convergent provided that neither hypersurface contains a nontrivial holomorphic variety. For higher codimensional generic submanifolds, convergence is proved e.g. under the assumption that the source is of finite type, the target does not contain a nontrivial holomorphic variety, and the mapping is finite. Finite determination (by jets of a predetermined order) of formal mappings between smooth generic submanifolds is also established.

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