On toric face rings
arXiv:math/0605150 · doi:10.1016/j.jpaa.2006.09.010
Abstract
Following a construction of Stanley we consider toric face rings associated to rational pointed fans. This class of rings is a common generalization of the concepts of Stanley--Reisner and affine monoid algebras. The main goal of this article is to unify parts of the theories of Stanley--Reisner- and affine monoid algebras. We consider (non-pure) shellable fan's and the Cohen--Macaulay property. Moreover, we study the local cohomology, the canonical module and the Gorenstein property of a toric face ring.
22 pages; Revised version of the paper
Cited by in corpus (11)
- Gröbner bases and Betti numbers of monoidal complexes
- Algebra retracts and Stanley-Reisner rings
- Seminormality and local cohomology of toric face rings
- On some local cohomology spectral sequences
- The geometry and combinatorics of cographic toric face rings
- On canonical modules of toric face rings
- Differential operators, retracts, and toric face rings
- Dualizing complex of a toric face ring
- Dualizing complexes of seminormal affine semigroup rings and toric face rings
- Higher Cohen-Macaulay property of squarefree modules and simplicial posets
- Dualizing Complex of a Toric Face Ring II: Non-normal Case