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

Ballico, Edoardo

Ann. Inst. Fourier 45, No. 4, 1119-1121 (1995).

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 \(F\).

MSC:

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

Keywords:

singular foliations; codimension 1 foliations; Kupka component; complete intersection; unstable vector bundle; rank 2 vector bundle; splitting of a vector bundle; meromorphic first integral; Barth-Lefschetz theorems

Citations:

Zbl 0811.32024

References:

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