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

• 成果类型: Article
• 署名作者: Gong, Xianghong; Stolovitch, Laurent
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Universite Cote d'Azur; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0654-8
• 发表日期: 2016
• 页码: 293-377
• 关键词: analytic surfaces; local hull; normalization; holomorphy; MANIFOLDS; STABILITY

摘要

We study a germ of real analytic n-dimensional submanifold of 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 that intersects a real submanifold along two totally and real analytic submanifolds that intersect transversally at a possibly non-isolated CR singularity.