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

Evelia R. García Barroso; Marcelo E. Hernandess; M. Fernando Hernández Iglesias

doi:10.2478/auom-2025-0021

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 33 (2025): Issue 2 (June 2025)

By: Evelia R. García Barroso , Marcelo E. Hernandess and M. Fernando Hernández Iglesias

Open Access

|Jun 2025

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2025-0021 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 107 - 124

Submitted on: Dec 1, 2024

Accepted on: Mar 15, 2025

Published on: Jun 3, 2025

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

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© 2025 Evelia R. García Barroso, Marcelo E. Hernandess, M. Fernando Hernández Iglesias, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 33 (2025): Issue 2 (June 2025)