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.
@article{urn:eudml:doc:41306,
title = {Some remarks on indices of holomorphic vector fields.},
journal = {Publicacions Matem\`atiques},
volume = {41},
year = {1997},
pages = {527-544},
mrnumber = {MR1485502},
zbl = {0912.32024},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41306}
}
Brunella, Marco. Some remarks on indices of holomorphic vector fields.. Publicacions Matemàtiques, Tome 41 (1997) pp. 527-544. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41306/