Transversely Lie holomorphic foliations on projective spaces
Complex Variables
2008-04-02 v1 Dynamical Systems
Abstract
We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection of codimension one foliations given by closed one-forms with simple poles. If there is only one singularity in a suitable affine space, then the foliation is induced by a linear diagonal vector field.
Cite
@article{arxiv.0804.0048,
title = {Transversely Lie holomorphic foliations on projective spaces},
author = {A. C. Mafra and B. Scardua},
journal= {arXiv preprint arXiv:0804.0048},
year = {2008}
}