Arithmetical ranks of stanley-reisner ideals of simplicial complexes with a cone

Margherita Barile, Naoki Terai

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

When a cone is added to a simplicial complex Δ over one of its faces, we investigate the relation between the arithmetical ranks of the Stanley-Reisner ideals of the original simplicial complex and the new simplicial complex Δ′. In particular, we show that the arithmetical rank of the Stanley-Reisner ideal of Δ′ equals the projective dimension of the Stanley-Reisner ring of Δ′ if the corresponding equality holds for Δ.

Original languageEnglish
Pages (from-to)3686-3698
Number of pages13
JournalCommunications in Algebra
Volume38
Issue number10
DOIs
Publication statusPublished - Oct 2010
Externally publishedYes

Keywords

  • Arithmetical rank
  • Monomial ideals
  • Projective dimension
  • Set-theoretic complete intersections

ASJC Scopus subject areas

  • Algebra and Number Theory

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