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Article Contents

# On the integrability of holomorphic vector fields

• We 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 $F$ : $(\mathbb{C}^{3},0)\rightarrow(\mathbb{C}^{2},0)$ such that the leaves of $\mathcal{F}_X$ are contained in the level curves of $F$.
Mathematics Subject Classification: Primary: 37F75; Secondary: 32H50, 32S65.

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