Mitera, Yoshiki; Yoshizaki, Junya The local analytical triviality of a complex analytic singular foliation. (English) Zbl 1074.32011 Hokkaido Math. J. 33, No. 2, 275-297 (2004). 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. Reviewer: Zbigniew Hajto (Kraków) Cited in 3 Documents 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) Keywords:singular foliation; local triviality; Whitney stratification PDFBibTeX XMLCite \textit{Y. Mitera} and \textit{J. Yoshizaki}, Hokkaido Math. J. 33, No. 2, 275--297 (2004; Zbl 1074.32011) Full Text: DOI