Flags of holomorphic foliations. (English) Zbl 1262.32021
Summary: A flag of holomorphic foliations on a complex manifold \(M\) is an object consisting of a finite number of singular holomorphic foliations on \(M\) of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft these objects and, in \(\mathbb P^n_{\mathbb C}\), \(n \geq 3\), we establish some necessary conditions for a foliation of lower dimension to leave invariant foliations of codimensions one. Finally, still in \(\mathbb P^n_{\mathbb C}\), we find bounds involving the degrees of polar classes of foliations in a flag.
MSC:
| 32M25 | Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions |
| 32S65 | Singularities of holomorphic vector fields and foliations |
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