## Nagoya Mathematical Journal

### Dualizing complex of a toric face ring

#### 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.

#### Article information

Source
Nagoya Math. J., Volume 196 (2009), 87-116.

Dates
First available in Project Euclid: 15 January 2010

https://projecteuclid.org/euclid.nmj/1263564649

Mathematical Reviews number (MathSciNet)
MR2591092

Zentralblatt MATH identifier
1183.13035

#### Citation

Okazaki, Ryota; Yanagawa, Kohji. Dualizing complex of a toric face ring. Nagoya Math. J. 196 (2009), 87--116. https://projecteuclid.org/euclid.nmj/1263564649

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