  The quantum plane $A=\mathbb{C}_\rho[x,y,z]$ with $\rho$ a root of unity has
singularities in its representation variety $\mathbf{trep}_nA$ and its center
$Z(A)$. Using the technique of a noncommutative blow-up, we prove that this
technique fails in contrast to the 3-dimensional Sklyanin algebras if we want
to resolve the singularities in the representation variety. However, we will
see that the singularity of the center in the origin can be made better using
this technique.
