TY - JOUR
T1 - Moduli spaces of germs of holomorphic foliations in the plane
AU - Maŕin, David
PY - 2003/9/1
Y1 - 2003/9/1
N2 - In this paper we study the topological moduli space of some germs of singular holomorphic foliations in (ℂ2, 0). We obtain a fully characterization for generic foliations whose vanishing order at the origin is two or three. We give a similar description for a certain subspace in the moduli space of generic germs of homogeneous foliations of any vanishing order and also for generic quasi-homogeneous foliations. In all the cases we identify the fundamental group of these spaces using the Gassner representation of the pure braid group and a suitable holonomy representation of the foliation.
AB - In this paper we study the topological moduli space of some germs of singular holomorphic foliations in (ℂ2, 0). We obtain a fully characterization for generic foliations whose vanishing order at the origin is two or three. We give a similar description for a certain subspace in the moduli space of generic germs of homogeneous foliations of any vanishing order and also for generic quasi-homogeneous foliations. In all the cases we identify the fundamental group of these spaces using the Gassner representation of the pure braid group and a suitable holonomy representation of the foliation.
KW - Moduli space
KW - Holonomy representation
KW - Holomorphic foliation
UR - https://dialnet.unirioja.es/servlet/articulo?codigo=2203637
UR - https://www.scopus.com/pages/publications/0042976438
U2 - 10.1007/s00014-003-0771-z
DO - 10.1007/s00014-003-0771-z
M3 - Article
SN - 0010-2571
VL - 78
SP - 518
EP - 539
JO - Commentarii Mathematici Helvetici
JF - Commentarii Mathematici Helvetici
ER -