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ONE-DIMENSIONAL LIE FOLIATIONS WITH GENERIC SINGULARITIES IN COMPLEX DIMENSION THREE

Part of: Differential topology

Published online by Cambridge University Press:  28 September 2011

ALBETÃ MAFRA  and
BRUNO SCARDUA
ALBETÃ MAFRA
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970-Rio de Janeiro, Brazil (email: albetan@im.ufrj.br)
BRUNO SCARDUA*
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21945-970-Rio de Janeiro, Brazil (email: scardua@im.ufrj.br)
*
✉For correspondence; e-mail: scardua@im.ufrj.br
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Abstract

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We prove that a germ of a one-dimensional holomorphic foliation with a generic singularity in dimension two or three that exhibits a Lie group transverse structure in the complement of some codimension one analytic subset is logarithmic, that is, given by a system of closed meromorphic one-forms with simple poles. In the global context, we prove that a foliation by curves in a three-dimensional complex manifold with generic singularities and a Lie group transverse structure off a codimension one analytic subset is logarithmic; that is, it is given by a system of closed meromorphic one-forms with simple poles.

Keywords

holomorphic foliation with singularitiesLie transverse structure

MSC classification

Secondary: 57R30: Foliations; geometric theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 91 , Issue 1 , August 2011 , pp. 13 - 28
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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