The topology of the generic polar curve and the Zariski invariant for branches of genus one
Evelia R. García Barroso
Departamento de Matemáticas, Estadística e I.O., IMAULL. Universidad de La Laguna, Apartado de Correos 456La Laguna, Tenerife, España
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, Marcelo E. Hernandess
Departamento de Matemática, Universidade Estadual de MaringáBrazil
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oraz M. Fernando Hernández Iglesias
Pontificia Universidad Católica del PerúPerú
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03 cze 2025
O artykule
Data publikacji: 03 cze 2025
Zakres stron: 107 - 124
Otrzymano: 01 gru 2024
Przyjęty: 15 mar 2025
DOI: https://doi.org/10.2478/auom-2025-0021
Słowa kluczowe
© 2025 Evelia R. García Barroso et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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.