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International conference «Real and Complex Dynamical Systems», dedicated to the to the 75th anniversary of Yu. S. Il'yashenko
November 30, 2018 14:50–15:20, Moscow, Steklov Mathematical Institute (Gubkina, 8, 9th floor)
 


On the classifcation of germs of foliations in $(\mathbb C^n,0)$

Èrnesto Rosales-González

Instituto de Matemáticas, Universidad Nacional Autónoma de México
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Èrnesto Rosales-González
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Abstract: We consider germs of holomorphic vector fields in $(\mathbb C^n,0), n\ge 3$, with non isolated singularities. We assume that the set of singular points forms a submanifold of codimension 2, and the sum of the nonzero eigenvalues of the linearization of the germs at each singular point is zero. We give the orbital analytic classification of generic germs of such type. It happens that the formal classification is trivial, and the analytic one has functional moduli, unlike the cases of dicritic and nondicritic generic germs in $n=2$ with isolated and degenerated singularity where the formal and analytical classification coincide [2],[3]. Joint work with Ortiz-Bobadilla, L. (UNAM, México); Voronin, S. M. (CSU, Russia).

Language: English

References
  1. Ortiz-Bobadilla, L.; Rosales-Gonzaléz, E.; Voronin, S. M., Analytic classification of foliations induced by germs of holomorphic vector fields in $(\mathbb C^n, 0)$ with nonisolated singularities
  2. Ortiz-Bobadilla, L.; Rosales-Gonzaléz, E.; Voronin, S. M., “Rigidity theorems for generic holomorphic germs of dicritic foliations and vector fields in $(\mathbb C^2, 0)$”, Mosc. Math. J., 5:1 (2005), 171–206
  3. Ortiz-Bobadilla, L.; Rosales-Gonzaléz, E.; Voronin, S. M., “Thom’s Problem for Degenerate Singular Points of Holomorphic Foliations in the Plane”, Mosc. Math. J., 12:4 (2012), 825–862


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