Separatrices for $\mathbb{C}^2$ actions on 3-manifolds

Rebelo, Julio C.; Reis, Helena

doi:10.4171/CMH/300

Commentarii Mathematici Helvetici

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Volume 88, Issue 3, 2013, pp. 677–714

DOI: 10.4171/CMH/300

Published online: 2013-08-13

Separatrices for $\mathbb{C}^2$ actions on 3-manifolds

Julio C. Rebelo^[1] and Helena Reis^[2]

(1) Université Toulouse 3, France
(2) Universidade do Porto, Portugal

We prove the existence of a separatrix for the codimension 1 singular foliation spanned by two commuting holomorphic vector fields on a neighborhood of the origin in $\mathbb{C}^3$.

Keywords: Invariant analytic surface, reduction of singularities, commuting vector fields

Rebelo Julio, Reis Helena: Separatrices for $\mathbb{C}^2$ actions on 3-manifolds. Comment. Math. Helv. 88 (2013), 677-714. doi: 10.4171/CMH/300