TY - JOUR
T1 - Nodal separators of holomorphic foliations
AU - Rosas, Rudy
N1 - Publisher Copyright:
© Association des Annales de l'institut Fourier, 2018, Certains droits réservés.
PY - 2018
Y1 - 2018
N2 - We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and topological equivalence for nodal separators as intrinsic objects and, in analogy with the celebrated theorem of Zariski for analytic curves, we prove the equivalence of these notions. We give some applications in the study of topological equivalences of holomorphic foliations. In particular, we show that the nodal singularities and its eigenvalues in the resolution of a generalized curve are topological invariants.
AB - We study a special kind of local invariant sets of singular holomorphic foliations called nodal separators. We define notions of equisingularity and topological equivalence for nodal separators as intrinsic objects and, in analogy with the celebrated theorem of Zariski for analytic curves, we prove the equivalence of these notions. We give some applications in the study of topological equivalences of holomorphic foliations. In particular, we show that the nodal singularities and its eigenvalues in the resolution of a generalized curve are topological invariants.
KW - Equisingularity
KW - Holomorphic foliation
KW - Topological equivalence
UR - http://www.scopus.com/inward/record.url?scp=85047482149&partnerID=8YFLogxK
U2 - 10.5802/aif.3168
DO - 10.5802/aif.3168
M3 - Article
AN - SCOPUS:85047482149
SN - 0373-0956
VL - 68
SP - 511
EP - 539
JO - Annales de l'Institut Fourier
JF - Annales de l'Institut Fourier
IS - 2
ER -