Construction of a Basis of K\"{a}hler differentials for generic plane branches

Let C be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the C[[x]]-module of K\"ahler differentials for generic Γ ∈ C, algorithmically, and study its behaviour under blow-up. As an application, we give an alternative proof for a formula of Genzmer, that provides the dimension of the generic component of the moduli of analytic classes in the equisingularity class of Γ.