Geometry of representations of quantum spaces

Abstract

The quantum plane A = Cρ[x, y, z] with ρ a root of unity has singularities in its representation variety trep n A and its center C[u,v,w,g] uvw−g n . 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 trep n A. However, we will see that the singularity of the center in the origin can be made better using this technique.