On canonical modules of toric face rings
Commutative Algebra
2021-05-18 v1 Combinatorics
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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Cite
@article{arxiv.math/0612650,
title = {On canonical modules of toric face rings},
author = {Bogdan Ichim and Tim Roemer},
journal= {arXiv preprint arXiv:math/0612650},
year = {2021}
}
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17 pages