×

The local analytical triviality of a complex analytic singular foliation. (English) Zbl 1074.32011

The authors investigate complex analytic singular foliations defined on the complex analytic manifold \(M\) of dimension \(n\). After recalling basic notions of the theory of singular foliations they prove a theorem about local analytic triviality along the leaves. The main tool of the proof is the Whitney stratification of the singular locus. The last section of the paper contains various examples which show the nature of the local analytic triviality of holomorphic foliations.

MSC:

32S65 Singularities of holomorphic vector fields and foliations
32C25 Analytic subsets and submanifolds
14B05 Singularities in algebraic geometry
32B15 Analytic subsets of affine space
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
PDFBibTeX XMLCite
Full Text: DOI