On the integrability of holomorphic vector fields

We determine topological and algebraic conditions for a germ of holomorphicfoliation $\mathcal F(X)$ induced by a generic vector field $X$ on$(\mathbb{C}^{3},0)$ to have a holomorphic first integral, i.e., a germ ofholomorphic map $F \colon(\mathbb{C}^{3},0)\longrightarrow(\mathbb{C}^{2},0)$such that the leaves of $\mathcal F(X)$ are contained in the level curves of$F$.