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Holomorphic normalization of Cartan type algebras of singular holomorphic vector fields. (Normalisation holomorphe d’algèbres de type Cartan de champs de vecteurs holomorphes singuliers.) (French) Zbl 1039.32042

The author deals with a commutative family of holomorphic vector fields and shows that such fields can be holomorphically normalized in a neighborhood of a common fixed point if a Diophantine condition related to the Lie algebra of linear vector fields associated to the linear parts of the elements of the family is satisfied as well as some algebraic assumptions on the normal form of the family are made. The elements of the family, but one, may not have a non-zero linear part.

MSC:

32S65 Singularities of holomorphic vector fields and foliations
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