Nodal separators of holomorphic foliations
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 511-539.

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.

Nous étudions un type particulier d’ensembles invariants locaux de feuilletages holomorphes singuliers appelés séparateurs nodaux. Nous définissons des notions d’équisingularité et d’équivalence topologique pour les séparateurs nodaux comme des objets intrinsèques et, par analogie avec le célèbre théorème de Zariski pour les courbes analytiques, nous prouvons l’équivalence de ces notions. Nous donnons quelques applications à l’étude des équivalences topologiques de feuilletages holomorphes. En particulier, nous montrons que les singularités nodales et ses valeurs propres dans la résolution d’une courbe généralisée sont des invariants topologiques.

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Accepted:
Published online:
DOI: 10.5802/aif.3168
Classification: 37F75, 34M35, 32S15
Keywords: Holomorphic foliation, topological equivalence, equisingularity
Mot clés : feuilletage holomorphe, conjugaison topologique, équisingularité
Rosas, Rudy 1

1 Pontificia Universidad Católica del Perú Av Universitaria 1801, Lima (Peru)
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Rosas, Rudy. Nodal separators of holomorphic foliations. Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 511-539. doi : 10.5802/aif.3168. http://archive.numdam.org/articles/10.5802/aif.3168/

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