%0 Journal Article
%T On formal maps between generic submanifolds in complex space
%A Jean-Charles Suny¨¦
%J Mathematics
%D 2009
%I arXiv
%R 10.1007/s12220-009-9085-8
%X 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.
%U http://arxiv.org/abs/0906.1955v1