Gorenstein rings through face rings of manifolds
Combinatorics
2014-01-14 v1 Commutative Algebra
Abstract
The face ring of a homology manifold (without boundary) modulo a generic system of parameters is studied. Its socle is computed and it is verified that a particular quotient of this ring is Gorenstein. This fact is used to prove that the sphere -conjecture implies all enumerative consequences of its far reaching generalization (due to Kalai) to manifolds. A special case of Kalai's manifold -conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.
Keywords
Cite
@article{arxiv.0806.1017,
title = {Gorenstein rings through face rings of manifolds},
author = {Isabella Novik and Ed Swartz},
journal= {arXiv preprint arXiv:0806.1017},
year = {2014}
}