Bogdan Ichim
,
Tim Römer
MSC 2000
- 13C14 Cohen-Macaulay modules
-
13D45 Local cohomology
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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