The Saito module and the moduli of a germ of curve in $\left(\mathbb{C}^{2},0\right)$

Abstract

We study properties of the module of vector fields tangent to a given germ of curve in the complex plane $\mathbb{C}^{2}$. As a consequence, we obtain a conjectural algorithm to compute the generic dimension of its moduli space. For some families of curves, we proved that this algorithm provides the correct dimension.