Desingularization of non-dicritical holomorphic foliations and existence of separatrices. (English) Zbl 0771.32018

The authors continue their earlier work [cf. the first author, C. R. Acad. Sci., Paris, Sér. I 307, No. 15, 795-798 (1988; Zbl 0669.32007)]; they have completed the reduction of the singularities for non-dicritical holomorphic foliations in order to get only the so-called simple singularities. As a consequence, they have proved R. Thom’s conjecture about the existence of convergent separatrices, in dimension three [cf. the authors, C. R. Acad. Sci., Paris, Sér. I Math. 307, 387-390 (1988; Zbl 0656.57019)].


32S30 Deformations of complex singularities; vanishing cycles
32S45 Modifications; resolution of singularities (complex-analytic aspects)
32S65 Singularities of holomorphic vector fields and foliations
57R30 Foliations in differential topology; geometric theory
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