I have a doubt, about prove the next result
Let $f\left( x,y\right)$ a polynomial irreducible in the local ring $O\left(\mathbb{C}^{2},0\right)$, let $\gamma=$ $\{$ $(x,y) \in \mathbb{C}^{2}:f(x,y)=0$ $\}$ then the differential $d\left.f\right\vert _{\gamma}$ vanishes only at the origin.
How prove the above result? I need only a bit hit...
regards!
