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.

MSC:

 34M05 Entire and meromorphic solutions to ordinary differential equations in the complex domain

Keywords:

singularities; flow; vector field; separatrix
Full Text:

References:

 [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
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