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arXiv · 2411.10853

The topology of the generic polar curve and the Zariski invariant for branches of genus one

Evelia R. García Barroso·Marcelo E. Hernandes·M. Fernando Hernández Iglesias
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Abstract

We study, for plane complex branches of genus one, the topological type of its generic polar curve, as a function of the semigroup of values and the Zariski invariant of the branch. We improve some results given by Casas-Alvero in 2023, since we filter the topological type fixed for the branch by the possible values of Zariski invariants.

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Evelia R. García Barroso, Marcelo E. Hernandes, M. Fernando Hernández Iglesias. 2024-11-16. The topology of the generic polar curve and the Zariski invariant for branches of genus one. https://arxiv.org/abs/2411.10853

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