REAL SUBMANIFOLDS OF MAXIMUM COMPLEX TANGENT SPACE AT A CR SINGULAR POINT, I - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Article Dans Une Revue Inventiones Mathematicae Année : 2016

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

Xianghong Gong
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Résumé

We study a germ 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 show its equivalence to a normal form under a local biholomorphism at the singularity. We also show that if a real submanifold is formally equivalent to a quadric, it is actually holomorphically equivalent to it, if a small divisors condition is satisfied. Finally, we investigate the existence of a complex submanifold of positive dimension in C n that intersects a real submanifold along two totally and real analytic submanifolds that intersect transversally at a possibly non-isolated CR singularity.
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Dates et versions

hal-01279021 , version 1 (25-02-2016)

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Xianghong Gong, Laurent Stolovitch. REAL SUBMANIFOLDS OF MAXIMUM COMPLEX TANGENT SPACE AT A CR SINGULAR POINT, I. Inventiones Mathematicae, 2016, 206, pp.293-377. ⟨10.1007/s00222-016-0654-8⟩. ⟨hal-01279021⟩
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