On formal maps between generic submanifolds in complex space

Details On formal maps between generic submanifolds in complex space On formal maps between generic submanifolds in complex space

2009-06-10

arxiv.org/abs/0906.1955v1

J. Geom. Anal. 19 (2009), no. 4, 944-962.

Mathematics

Complex Variables

Scientific paper

10.1007/s12220-009-9085-8

Let H:(M,p)->(M',p') be a formal mapping between two germs of real-analytic generic submanifolds in C^N with nonvanishing Jacobian. Assuming M to be minimal at p and M' holomorphically nondegenerate at p', we prove the convergence of the mapping H. As a consequence, we obtain a new convergence result for arbitrary formal maps between real-analytic hypersurfaces when the target does not contain any holomorphic curve. In the case when both M and M' are hypersurfaces, we also prove the convergence of the associated reflection function when M is assumed to be only minimal. This allows us to derive a new Artin type approximation theorem for formal maps of generic full rank.

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