Real submanifolds of maximum complex tangent space at a CR singular point, II

Xianghong Gong; Laurent Stolovitch

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arXiv · 1610.03297

Real submanifolds of maximum complex tangent space at a CR singular point, II

Xianghong Gong·Laurent Stolovitch

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Abstract

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 the condition that its complexification admits the maximum number of deck transformations, we first classify holomorphically its quadratic CR singularity. We then study its transformation to a normal form under the action of local (possibly formal) biholomorphisms at the singularity. We first conjugate formally its associated reversible map $σ$ to suitable normal forms and show that all these normal forms can be divergent. We then construct a unique formal normal form under a non degeneracy condition.

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BibTeX RIS

Xianghong Gong, Laurent Stolovitch. 2016-10-11. Real submanifolds of maximum complex tangent space at a CR singular point, II. https://arxiv.org/abs/1610.03297

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