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 language | English |
---|---|
Pages (from-to) | 711-730 |
Number of pages | 20 |
Journal | Advances in Mathematics |
Volume | 229 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jan 30 2012 |
Externally published | Yes |
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)