Mathematics – Commutative Algebra
Scientific paper
2006-12-21
Nagoya Math. J. 194, 69-90 (2009)
Mathematics
Commutative Algebra
17 pages
Scientific paper
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.
Ichim Bogdan
Roemer Tim
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