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...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2025-06-01
|
| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2025-0021 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849727322383450112 |
|---|---|
| author | García Barroso Evelia R. Hernandess Marcelo E. Fernando Hernández Iglesias M. |
| author_facet | García Barroso Evelia R. Hernandess Marcelo E. Fernando Hernández Iglesias M. |
| author_sort | García Barroso Evelia R. |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d297459398fd4329a14f2d6876cd161b |
| institution | DOAJ |
| issn | 1844-0835 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj-art-d297459398fd4329a14f2d6876cd161b2025-08-20T03:09:52ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352025-06-0133210712410.2478/auom-2025-0021The topology of the generic polar curve and the Zariski invariant for branches of genus oneGarcía Barroso Evelia R.0Hernandess Marcelo E.1Fernando Hernández Iglesias M.21Departamento de Matemáticas, Estadística e I.O., IMAULL. Universidad de La Laguna, Apartado de Correos 456. 38200La Laguna, Tenerife, España.2Departamento de Matemática, Universidade Estadual de Maringá, Avenida Colombo 5790. Maringá-PR 87020-900. Brazil.3Pontificia Universidad Católica del Perú, Av. Universitaria 1801, San Miguel 15088, Perú.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.https://doi.org/10.2478/auom-2025-0021plane brancheszariski invariantgeneric polar curvetopological typeprimary 14h20secondary 32s10 |
| spellingShingle | García Barroso Evelia R. Hernandess Marcelo E. Fernando Hernández Iglesias M. The topology of the generic polar curve and the Zariski invariant for branches of genus one Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica plane branches zariski invariant generic polar curve topological type primary 14h20 secondary 32s10 |
| title | The topology of the generic polar curve and the Zariski invariant for branches of genus one |
| title_full | The topology of the generic polar curve and the Zariski invariant for branches of genus one |
| title_fullStr | The topology of the generic polar curve and the Zariski invariant for branches of genus one |
| title_full_unstemmed | The topology of the generic polar curve and the Zariski invariant for branches of genus one |
| title_short | The topology of the generic polar curve and the Zariski invariant for branches of genus one |
| title_sort | topology of the generic polar curve and the zariski invariant for branches of genus one |
| topic | plane branches zariski invariant generic polar curve topological type primary 14h20 secondary 32s10 |
| url | https://doi.org/10.2478/auom-2025-0021 |
| work_keys_str_mv | AT garciabarrosoeveliar thetopologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone AT hernandessmarceloe thetopologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone AT fernandohernandeziglesiasm thetopologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone AT garciabarrosoeveliar topologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone AT hernandessmarceloe topologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone AT fernandohernandeziglesiasm topologyofthegenericpolarcurveandthezariskiinvariantforbranchesofgenusone |