# Some remarks on indices of holomorphic vector fields.

Publicacions Matemàtiques (1997)

- Volume: 41, Issue: 2, page 527-544
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topBrunella, Marco. "Some remarks on indices of holomorphic vector fields.." Publicacions Matemàtiques 41.2 (1997): 527-544. <http://eudml.org/doc/41306>.

@article{Brunella1997,

abstract = {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.},

author = {Brunella, Marco},

journal = {Publicacions Matemàtiques},

keywords = {Campos vectoriales; Funciones holomorfas; Puntos singulares; holomorphic vector field; isolated singularity; Baum-Bott index; intersection index; Poincaré-Hopf index},

language = {eng},

number = {2},

pages = {527-544},

title = {Some remarks on indices of holomorphic vector fields.},

url = {http://eudml.org/doc/41306},

volume = {41},

year = {1997},

}

TY - JOUR

AU - Brunella, Marco

TI - Some remarks on indices of holomorphic vector fields.

JO - Publicacions Matemàtiques

PY - 1997

VL - 41

IS - 2

SP - 527

EP - 544

AB - 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.

LA - eng

KW - Campos vectoriales; Funciones holomorfas; Puntos singulares; holomorphic vector field; isolated singularity; Baum-Bott index; intersection index; Poincaré-Hopf index

UR - http://eudml.org/doc/41306

ER -