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arXiv · 0710.4774

On the integrability of holomorphic vector fields

Leonardo Camara·Bruno Scardua
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Abstract

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 $F \colon(\mathbb{C}^{3},0)\longrightarrow(\mathbb{C}^{2},0)$ such that the leaves of $\mathcal F(X)$ are contained in the level curves of $F$.

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Leonardo Camara, Bruno Scardua. 2007-10-25. On the integrability of holomorphic vector fields. https://arxiv.org/abs/0710.4774

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