To each isolated singularity of hypersurface of dimension $n$, one associates the local fundamental group $G$ of the moduli space minus the discriminant locus, and a representation $\sigma : G \to \text{Aut} \, (H)$, where $H$ is the $n$-homology group, with integer coefficient, of the "non singular fibre". Although in general it is very difficult to determine even a presentation of $G$, we show that the image of $\sigma$ can be fairly rather easily, by using some relations in a first approximative presentation of $G$, in the case of polynomials of the type $x_{0}^{a_{0}} + \cdots + x_{n}^{a_{n}}$. We solve in this way a conjecture of Arnold, Brieskorn [1].