  We investigate the face numbers of simplicial complexes with Buchsbaum vertex
links, especially pseudomanifolds with isolated singularities. This includes
deriving Dehn-Sommerville relations for pseudomanifolds with isolated
singularities and establishing lower bound theorems when the singularities are
also homologically isolated. We give formulas for the Hilbert function of a
generic Artinian reduction of the face ring when the singularities are
homologically isolated and for any pure two-dimensional complex. Some examples
of spaces where the $f$-vector can be completely characterized are described.
Let $\Delta$ and $\Delta'$ be two simplicial complexes that are homeomorphic
and have the same $f$-vector. In \cite{MNS} the question is raised of whether
or not the Hilbert functions of generic Artinian reductions of their face rings
are identical. We prove that this is the case if the spaces have isolated
singularities and are PL-homeomorphic.
