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Topological type of discriminants of some special families
(Springer Science+Business Media, 2021-09-08)
We will describe the topological type of the discriminant curve of the morphism $$(\ell , f)$$ ( ℓ , f ) , where $$\ell $$ ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.
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Weierstrass 1-Forms and Nondicritical Generalized Curve Foliations
(World Scientific, 2023-05-01)
In this paper, we introduce a distinguished expression for a given 1-form with respect to a polynomial f ∈ C{x}[y], called Weierstrass form. We will use this form and the properties of plane analytical curves to give new characterizations of nondicritical generalized curve foliations.

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