Holomorphic foliations and Kupka singular sets
Let \({\mathcal F}\) be a holomorphic codimension one foliation on a complex manifold \(M\) with the singularity \(\text{sing}({\mathcal F})\). The authors investigate the structure on the neighborhood of \(\text{sing} ({\mathcal F})\). After recalling the definition of the Kupka subset \(K({\mathcal F})\) of \(\text{sing}({\mathcal F})\) and summarizing the main properties of the Kupka subsets, the authors give some conditions for \({\mathcal F}\) to have an affine transverse or a projective transverse structure for \({\mathcal F}\) in a neighborhood of \(K({\mathcal F})\). The conditions are given by geometric properties for certain codimension 2 analytic subset \(S\) in \(\text{sing} ({\mathcal F})\).
scientific article; zbMATH DE number 1339901