A note on cohen-macaulayness of stanley-reisner rings with serre's condition (S2)

Naoki Terai, Ken Ichi Yoshida

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Let be a (d-1)-dimensional simplicial complex on the vertex set V={1, 2, n}. In this article, using Alexander duality, we prove that the Stanley-Reisner ring k[Δ] is Cohen-Macaulay if it satisfies Serre's condition (S2) and the multiplicity e(k[Δ]) is "sufficiently large", that is, [image omitted]. We also prove that if e(k[Δ])3d-2 and the graded Betti number 2, d+2(k[Δ]) vanishes, then the Castelnuovo-Mumford regularity regk[Δ] is less than d.

Original languageEnglish
Pages (from-to)464-477
Number of pages14
JournalCommunications in Algebra
Volume36
Issue number2
DOIs
Publication statusPublished - Feb 2008
Externally publishedYes

Keywords

  • Alexander duality
  • Cohen-Macaulay
  • Initial degree
  • Linear resolution
  • Multiplicity
  • Relation type
  • Serre's condition
  • Stanley-Reisner ring

ASJC Scopus subject areas

  • Algebra and Number Theory

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