Face numbers of pseudomanifolds with isolated singularities

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 and upper 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 twodimensional complex. Some examples of spaces where the f -vector can be completely characterized are described. We also show that the Hilbert function of a generic Artinian reduction of the face ring of a simplicial complex ∆ with isolated singularities minus the h-vector of ∆ is a PL-topological invariant. 2010 Mathematics Subject Classification. 05E45, 13F55, 05E40, 13D45