2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140783We determine topological and algebraic conditions for a germ of holomorphic foliation $\mathcal F(X)$ induced by a generic vector field $X$ on $(\mathbb{C}^{3},0)$ to have a holomorphic first integral, i.e., a germ of holomorphic 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 $F$.14 pages, 1 figureComplex Variables37F75, 32M25, 32S65text