Some remarks on indices of holomorphic vector fields

Autores: Marco Brunella
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 527-544
Idioma: inglés
DOI: 10.5565/publmat_41297_17
Títulos paralelos:
- Observaciones sobre índices de campos vectoriales holomórficos
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Resumen
- One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation.