  Given a Cayley-Hamilton smooth order A in a central simple algebra $\Sigma$,
we determine the flat locus of the Brauer-Severi fibration of the smooth order.
Moreover, we give a classification of all (reduced) central singularities where
the flat locus differs from the Azumaya locus and show that the fibers over the
flat, non-Azumaya points near these central singularities can be described as
fibered products of graphs of projection maps, thus generalizing an old result
of Artin on the fibers of the Brauer-Severi fibration over a ramified point.
Finally, we show these fibers are also toric quiver varieties and use this fact
to compute their cohomology.
