Some remarks on indices of holomorphic vector fields.

Brunella, 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 -