REVIEW 2 cited by
Normal Rees algebras arising from vertex decomposable simplicial complexes
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
We show that for a vertex decomposable simplicial complex $\Delta$, the Rees algebra of $I_{\Delta^{\vee}}$ is a normal Cohen-Macaulay domain. As consequences, we show that any squarefree weakly polymatroidal ideal is normal and we obtain normal ideals among several interesting families of monomial ideals such as cover ideals of graphs and edge ideals of hypergraphs. Moreover, based on a construction on simplicial complexes given by Biermann and Van Tuyl [2], we present families of normal ideals attached to any squarefree monomial ideal.
Forward citations
Cited by 2 Pith papers
-
Principal vector-spread Borel ideals
For squarefree principal vector-spread Borel ideals, the paper gives the minimal primary decomposition, proves sequential Cohen-Macaulayness, and classifies normal torsionfreeness via the index bounds j_i <= sum_{s<=i} t_s.
-
Sortable simplicial complexes and their associated toric rings
Every d-flag sortable simplicial complex is claimed to be vertex decomposable, and its associated toric and Rees algebras are Koszul, normal Cohen-Macaulay domains.
Discussion (0). Continue with ORCID to comment.