Geodesic
Family of intersecting totally real manifolds of (ℂn,0) and germs of holomorphic diffeomorphisms
[Famille d'intersection de variétés totalement réelles de (ℂn,0) et singularités CR]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 247-263

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We prove the existence (and give a characterization) of a germ of complex analytic set left invariant by an abelian group of germs of holomorphic diffeomorphisms at a common fixed point.We also give condition that ensure that such a group can be linearized holomorphically near the fixed point. It rests on a “small divisors condition” of the family of linear parts.

The second part of this article is devoted to the study families of totally real intersecting n-submanifolds of (ℂn,0). We give some conditions which allow to straighten holomorphically the family. If it is not possible to do this formally, we construct a germ of complex analytic set at the origin which intersection with the family can be holomorphically straightened. The second part is an application of the first.

@article{BSMF_2015__143_2_247_0,
     author = {Stolovitch, Laurent},
     title = {Family of intersecting totally real manifolds of~$({\mathbb {C}}^n,0)$ and germs of holomorphic diffeomorphisms},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {247--263},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {2},
     year = {2015},
     doi = {10.24033/bsmf.2685},
     mrnumber = {3351178},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2685/}
}
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Stolovitch, Laurent. Family of intersecting totally real manifolds of $({\mathbb {C}}^n,0)$ and germs of holomorphic diffeomorphisms. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 247-263. doi: 10.24033/bsmf.2685

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