  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
