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2009 On canonical modules of toric face rings
Bogdan Ichim, Tim Römer
Nagoya Math. J. 194: 69-90 (2009).

Abstract

Generalizing the concepts of Stanley-Reisner and affine monoid algebras, one can associate to a rational pointed fan $\Sigma$ in $\mathbb{R}^{d}$ the $\mathbb{Z}^{d}$-graded toric face ring $K[\Sigma]$. Assuming that $K[\Sigma]$ is Cohen-Macaulay, the main result of this paper is to characterize the situation when its canonical module is isomorphic to a $\mathbb{Z}^{d}$-graded ideal of $K[\Sigma]$. From this result several algebraic and combinatorial consequences are deduced. As an application, we give a relation between the cleanness of $K[\Sigma]$ and the shellability of $\Sigma$.

Citation

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Bogdan Ichim. Tim Römer. "On canonical modules of toric face rings." Nagoya Math. J. 194 69 - 90, 2009.

Information

Published: 2009
First available in Project Euclid: 17 June 2009

zbMATH: 1194.13012
MathSciNet: MR2536527

Subjects:
Primary: 13C14, 13D45
Secondary: 05E99

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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