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arXiv · math/0612650

On canonical modules of toric face rings

Bogdan Ichim·Tim Roemer
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Abstract

Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan the toric face ring. Assuming that this ring is Cohen-Macaulay, the main result of this paper is to characterize the situation when its canonical module is isomorphic to a fine graded ideal of the toric face ring. From this result several algebraic and combinatorial consequences are deduced in the situations where the fan may be related to a manifold with non-empty boundary, or the fan is a shellable fan.

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Bogdan Ichim, Tim Roemer. 2006-12-21. On canonical modules of toric face rings. https://doi.org/10.1017/s0027763000009636

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