On toric face rings

Details On toric face rings On toric face rings

2006-05-05

arxiv.org/abs/math/0605150v2

J. Pure Appl. Algebra 210, No. 1, 249-266 (2007)

Mathematics

Commutative Algebra

22 pages; Revised version of the paper

Scientific paper

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.

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