2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)
Dynamical Systems
2014-10-15 v1 Complex Variables
Abstract
We show that holomorphic vector fields on (C^3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra. In turn, this result enables us to show that the second jet of a holomorphic vector field defined on a compact complex manifold M of dimension 3 cannot vanish at an isolated singular point provided that M carries more than a single holomorphic vector field.
Keywords
Cite
@article{arxiv.1410.3527,
title = {2-dimensional Lie algebras and separatrices for vector fields on (C^3,0)},
author = {Julio C. Rebelo and Helena Reis},
journal= {arXiv preprint arXiv:1410.3527},
year = {2014}
}