On canonical modules of toric face rings

Details On canonical modules of toric face rings On canonical modules of toric face rings

2006-12-21

arxiv.org/abs/math/0612650v1

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.

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