Determination of the polar equisingularity type. (Détermination du type d’équisingularité polaire.) (French. English summary) Zbl 1116.32021
Summary: The equisingularity type of a generic polar of a curve \(C \subset (\mathbb {C}^2,0)\) is not determined by the type of \(C\). We expand the category of curves by associating to C the corresponding Hamiltonian foliation. In this way, we work in the less rigid frame of the space of foliations having C as invariant curve. We characterize kind types of equisingularity for C for which we completely determine the generic polar equisingularity type. The Hamiltonian case, corresponding to the classical theory of polar curves, can be special and sometimes does not provide the generic type.
MSC:
| 32S15 | Equisingularity (topological and analytic) |
| 37F75 | Dynamical aspects of holomorphic foliations and vector fields |
Keywords:
Hamiltonian foliationReferences:
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