Nodal separators of holomorphic foliations

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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.

Original languageEnglish
Pages (from-to)511-539
Number of pages29
JournalAnnales de l'Institut Fourier
Issue number2
StatePublished - 2018


  • Equisingularity
  • Holomorphic foliation
  • Topological equivalence


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