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

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