Dualizing complex of a toric face ring
Ryota Okazaki and Kohji Yanagawa
Source: Nagoya Math. J. Volume 196
(2009), 87-116.
Abstract
A toric face ring, which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Römer and their coauthors recently. In this paper, under the "normality" assumption, we describe a dualizing complex of a toric face ring $R$ in a very concise way. Since $R$ is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory over $R$, and show that the Cohen-Macaulay, Buchsbaum, and Gorenstein* properties of $R$ are topological properties of its associated cell complex.
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Permanent link to this document: http://projecteuclid.org/euclid.nmj/1263564649
Zentralblatt MATH identifier: 05660795
Mathematical Reviews number (MathSciNet): MR2591092
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