  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.
