On formal maps between generic submanifolds in complex space

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

Compte rendu de lecture de DEPAULE Jean-­‐Charles, À travers le mur, Marseille, éditions Parenthèses, collection Eupalinos, 2014, 219 p.

International audienceCompte rendu de lecture par Anna Madoeuf, septembre 2014, de DEPAULE Jean-­‐Charles, À travers le mur, Marseille, éditions Parenthèses, collection Eupalinos, 2014, 219 p