Singularités des flots holomorphes. (Singularities of holomorphic flows.). (French) Zbl 0853.34002

Summary: We get an obstruction to extend a germ of a holomorphic vector field to a complete holomorphic vector field. In particular, we prove that any isolated singularity of a complete holomorphic vector field on a complex surface has a non trivial second jet.


34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain
Full Text: DOI Numdam EuDML


[1] C. CAMACHO & P. SAD, Invariant varieties through singularities of holomorphic vector fields, Annals of Math., 115 (1982). · Zbl 0503.32007
[2] J. DIEUDONNÉ, Éléments d’analyse, Tome 4, Gauthier-Villars, 1971.
[3] X. GOMEZ-MONT & I. LUENGO, Germs of holomorphic vector fields in C3 without a separatrix, Inv. Math., 109 (1992). · Zbl 0774.32019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.