7 citations · 13 across the 23 of their papers we have counts for
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Constructive solution of Zariski's Moduli Problem for Plane Branches
Pedro Fortuny Ayuso, Javier Ribón
In this paper we give an explicit solution to Zariski's moduli problem for plane branches. We compute (in an algorithmic way) the set of Kähler differentials of an irreducible germ…
Explicit Computation of The Generic Component of the Analytic Moduli of a Plane Branch
Pedro Fortuny Ayuso, Javier Ribón
Let be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the -module of Kähler differentia…
Isotopy equivalence of analytic branches in
Pedro Fortuny Ayuso
We prove that two analytic branches in whose dual resolution graph is the same admit an ambient isotopy which is smooth outside the origin. A weaker version of t…
On the number of Puiseux exponents of an invariant branch of a vector field
Pedro Fortuny Ayuso
We show that the multiplicity of a plane analytic 1-form is a bound for the number of Puiseux exponents of a (formal or convergent) branch. This is true whether the associated foli…
Analytic Moduli of Plane Branches and Holomorphic Flows
Pedro Fortuny Ayuso, Javier Ribón
We study the behaviour (in the infinitesimal neighbourhood of the singularity) of a singular plane branch under the action of holomorphic flows. The techniques we develop provide a…
Vector flows and the analytic moduli of singular plane branches
Pedro Fortuny Ayuso
We provide a geometric elementary proof of the fact that an analytic plane branch is analytically equivalent to one whose terms corresponding to contacts with holomorphic one-forms…