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

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

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 th...

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Bibliographic Details
Main Authors: García Barroso Evelia R., Hernandess Marcelo E., Fernando Hernández Iglesias M.
Format: Article
Language:English
Published: Sciendo 2025-06-01
Series:Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica
Subjects:
plane branches
zariski invariant
generic polar curve
topological type
primary 14h20
secondary 32s10
Online Access:https://doi.org/10.2478/auom-2025-0021
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Summary: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.
ISSN:1844-0835

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