A splitting theorem for the Kupka component of a foliation of \({\mathbb{C}}{\mathbb{P}}^n, n\geq 6\). Addendum to an addendum to a paper by Calvo-Andrade and Soares. (English) Zbl 0959.32037

Ballico, Edoardo

Ann. Inst. Fourier 49, No. 4, 1423-1425 (1999).

Summary: Here we show that a Kupka component \(K\) of a codimension 1 singular foliation \(F\) of \({\mathbb{C}}{\mathbb{P}}^n, n\geq 6\) is a complete intersection. The result implies the existence of a meromorphic first integral of \(F\). The result was previously known if \(\text{deg}(K)\) was assumed to be not a square.
See the author’s earlier addendum [ibid. 45, 1119-1121 (1985; Zbl 0831.58046)].

MSC:

32S65	Singularities of holomorphic vector fields and foliations
37F75	Dynamical aspects of holomorphic foliations and vector fields
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; Zbl 0831.58046

References:

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