A splitting theorem for the Kupka component of a foliation of \({\mathbb{C}} {\mathbb{P}}^ n, n\geq 6\). Addendum to a paper by O. Calvo-Andrade and M. Soares. (English) Zbl 0831.58046

Summary: In this addendum of the paper by O. Calvo-Andrade and M. Soares [ibid. 44, 1219-1236 (1994; Zbl 0811.32024)], we show that a Kupka component \(K\) of a codimension 1 singular foliation \(F\) of \(\mathbb{C} \mathbb{P}^n\), \(n\geq 6\) with \(\deg (K)\) not a square is a complete intersection. The result implies the existence of a meromorphic first integral of \(F\).


37F75 Dynamical aspects of holomorphic foliations and vector fields
32S65 Singularities of holomorphic vector fields and foliations
14M10 Complete intersections
57R20 Characteristic classes and numbers in differential topology


Zbl 0811.32024
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