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On toric face rings

Bogdan Ichim·Tim Roemer
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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.

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Bogdan Ichim, Tim Roemer. 2006-05-05. On toric face rings. https://doi.org/10.1016/j.jpaa.2006.09.010

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