Local Cohomology of Stanley–Reisner Rings with Supports in General Monomial Ideals
✍ Scribed by Victor Reiner; Volkmar Welker; Kohji Yanagawa
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 224 KB
- Volume
- 244
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
We study the local cohomology modules H k ⌬ of the Stanley᎐Reisner ring
w x k ⌬ of a simplicial complex ⌬ with support in the ideal I ; k ⌬ corresponding ⌺ to a subcomplex ⌺ ; ⌬. We give a combinatorial topological formula for the multigraded Hilbert series, and in the case where the ambient complex is Gorenstein, compare this with a second combinatorial formula that generalizes results of Mustata and Terai. The agreement between these two formulae is seen to be a disguised form of Alexander duality. Other results include a comparison of the local cohomology with certain Ext modules, results about when it is concentrated in a single homological degree, and combinatorial topological interpretations of some vanishing theorems.