Affordable Access

Publisher Website

Local Cohomology of Stanley–Reisner Rings with Supports in General Monomial Ideals

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
244
Issue
2
Identifiers
DOI: 10.1006/jabr.2001.8932
Keywords
  • Stanley–Reisner Rings
  • Local Cohomology Modules
  • Alexander Duality
  • Lichtenbaum–Hartshorne Vanishing Theorem
  • Gorenstein Complex
Disciplines
  • Mathematics

Abstract

Abstract We study the local cohomology modules HiIΣ(k[Δ]) of the Stanley–Reisner ring k[Δ] of a simplicial complex Δ with support in the ideal IΣ⊂k[Δ] corresponding to a subcomplex Σ⊂Δ. 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.

There are no comments yet on this publication. Be the first to share your thoughts.