Groups of formal diffeomorphisms in several complex variables and closed one-forms

Details Groups of formal diffeomorphisms in several complex variables and closed one-forms Groups of formal diffeomorphisms in several complex variables and closed one-forms

2010-12-14

arxiv.org/abs/1012.3070v2

Mathematics

Complex Variables

The paper must be replaced by a new version, which is much more complete and clear, avoiding some notation mistakes

Scientific paper

We study groups of formal diffeomorphisms in several complex variables. For abelian, metabelian or nilpotent groups we investigate the existence of suitable formal vector fields and closed differential forms which exhibit an invariance property under the group action. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension.

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