Cohen-Macaulayness of large powers of Stanley-Reisner ideals

Naoki Terai, Ngo Viet Trung

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)

Abstract

We prove that for m≥3, the symbolic power Iδ(m) of a Stanley-Reisner ideal is Cohen-Macaulay if and only if the simplicial complex δ is a matroid. Similarly, the ordinary power Iδm is Cohen-Macaulay for some m≥3 if and only if Iδ is a complete intersection. These results solve several open questions on the Cohen-Macaulayness of ordinary and symbolic powers of Stanley-Reisner ideals. Moreover, they have interesting consequences on the Cohen-Macaulayness of symbolic powers of facet ideals and cover ideals.

Original languageEnglish
Pages (from-to)711-730
Number of pages20
JournalAdvances in Mathematics
Volume229
Issue number2
DOIs
Publication statusPublished - Jan 30 2012
Externally publishedYes

Keywords

  • Buchsbaum
  • Cohen-Macaulay
  • Complete intersection
  • Cover ideal
  • Facet ideal
  • Generalized Cohen-Macaulay
  • Matroid
  • Power
  • Serre condition (S)
  • Stanley-Reisner ideal

ASJC Scopus subject areas

  • Mathematics(all)

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