Abelian singularities of holomorphic Lie-foliations

Albetã Mafra and Bruno Scárdua

Journal of Singularities
volume 10 (2014), 191-199

Received 29 October 2012. Received in revised form 15 October 2014.

DOI: 10.5427/jsing.2014.10m

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We study holomorphic foliations with generic singularities and Lie group transverse structure outside of some invariant codimension one analytic subset. We introduce the concept of abelian singularity and prove that, for this type of singularities, the foliation is logarithmic. The Lie transverse structure is then used to extend the local (logarithmic) normal form from a neighborhood of the singularity, to the whole manifold.

Author(s) information:

Albetã Mafra Bruno Scárdua
Instituto de Matemática C.P. 68530, Instituto de Matemática C.P. 68530
Universidade Federal do Rio de Janeiro Universidade Federal do Rio de Janeiro
21.945-970 Rio de Janeiro-RJ, BRAZIL 21.945-970 Rio de Janeiro-RJ, BRAZIL
email: albetan@im.ufrj.br email: scardua@im.ufrj.br