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

Published 16 Nov 2024 in math.AG | (2411.10853v1)

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.

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