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2009 Dualizing complex of a toric face ring
Ryota Okazaki, Kohji Yanagawa
Nagoya Math. J. 196(none): 87-116 (2009).

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.

Citation

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Ryota Okazaki. Kohji Yanagawa. "Dualizing complex of a toric face ring." Nagoya Math. J. 196 87 - 116, 2009.

Information

Published: 2009
First available in Project Euclid: 15 January 2010

zbMATH: 1183.13035
MathSciNet: MR2591092

Subjects:
Primary: 13D25, 13F55

Rights: Copyright © 2009 Editorial Board, Nagoya Mathematical Journal

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Vol.196 • 2009
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