Face numbers of pseudomanifolds with isolated singularities

Details Face numbers of pseudomanifolds with isolated singularities Face numbers of pseudomanifolds with isolated singularities

2010-04-28

arxiv.org/abs/1004.5100v1

Mathematics

Combinatorics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Face numbers of pseudomanifolds with isolated singularities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Face numbers of pseudomanifolds with isolated singularities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Face numbers of pseudomanifolds with isolated singularities will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69347