  Let X be a singular affine normal variety with coordinate ring R and assume
that there is an R-order admitting a stability structure such that the scheme
of relevant semistable representations is smooth, then we construct a partial
desingularization of X with classifiable remaining singularities. In dimension
3 this explains the omnipresence of conifold singularities in partial
desingularizations of quotient singularities. In higher dimensions we have a
small list of singularity types generalizing the role of the conifold
singularity.
