Gorenstein rings through face rings of manifolds
By Isabella Novik, Ed Swartz. Compositio Mathematica, 2008
49 citations recorded by the source corpus.
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 algebraic g-conjecture for spheres implies all enumerative consequences of its far-reaching generalization (due to Kalai) to manifolds. A special case of Kalai’s conjecture is established for homology manifolds that have a codimension-two face whose link contains many vertices.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b862bf0d944a3437608884c67218831102323285
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Combinatorial Lefschetz theorems beyond positivity (2018, background): “mediately Lemma 3.7. For closed (d−1)-manifolds Min Rdwe have Soc(M) ∼=Hd(P•(M)) Proof. This is immediate from Lemma3.6. We have the following useful observation of Novik and Swartz: Proposition 3.8 ([NS09a]). For a triangulated (d−1)-dimensional rational manifold Min Rd, A∗(M) . Soc◦(M) is a Poinca”