Rebelo, Julio C. Singularités des flots holomorphes. (Singularities of holomorphic flows.). (French) Zbl 0853.34002 Ann. Inst. Fourier 46, No. 2, 411-428 (1996). 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. Cited in 4 ReviewsCited in 24 Documents MSC: 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain Keywords:singularities; flow; vector field; separatrix PDFBibTeX XMLCite \textit{J. C. Rebelo}, Ann. Inst. Fourier 46, No. 2, 411--428 (1996; Zbl 0853.34002) Full Text: DOI Numdam EuDML References: [1] [1] & , Invariant varieties through singularities of holomorphic vector fields, Annals of Math., 115 (1982). · Zbl 0503.32007 [2] [2] , Éléments d’analyse, Tome 4, Gauthier-Villars, 1971. · Zbl 0268.62001 [3] [3] & , 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.