On the integrability of holomorphic vector fields

Details On the integrability of holomorphic vector fields On the integrability of holomorphic vector fields

2007-10-25

arxiv.org/abs/0710.4774v1

Mathematics

Complex Variables

14 pages, 1 figure

Scientific paper

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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