Smooth order singularities

In this paper we give methods to classify the central singularities of Cayley-Hamilton smooth orders up to smooth equivalence in arbitrary central dimension. We prove that there is just one type in dimension 3 (the conifold singularity), three types in dimension 4, ten types in dimension 5 and 53 types in dimension 6. As the classification in dimension 5 and 6 is xy-pic intensive, we refer for the details to the full version of this paper, available at ftp://wins.uia.ac.be/pub/preprints/02/SOSfull.pdf