REAL SUBMANIFOLDS OF MAXIMUM COMPLEX TANGENT SPACE AT A CR SINGULAR POINT, II

摘要

We study germs of real analytic n-dimensional submanifold of C-n that has a complex tangent space of maximal dimension at a CR singularity. Under some assumptions, we first classify holo-morphically the quadrics having this property. We then study higher order perturbations of these quadrics and their transformations to a normal form under the action of local (possibly formal) biholomorphisms at the singularity. We are led to study formal Poincare-Dulac normal forms (non-unique) of reversible biholomorphisms. We exhibit a reversible map of which the normal forms are all divergent at the singularity. We then construct a unique formal normal form of the submanifolds under a non degeneracy condition.