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

García Barroso E.R.; Hernandess M.E.; Fernando Hernández Iglesias M. · Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica (2025) · DOI: 10.2478/auom-2025-0021

Resumen

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.

Instituciones: Pontificia Universidad Católica del Perú