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Dualizing Complex of a Toric Face Ring

Published online by Cambridge University Press:  11 January 2016

Ryota Okazaki  and
Kohji Yanagawa
Ryota Okazaki
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology Osaka University Toyonaka, Osaka, 560-0043, Japan, u574021d@ecs.cmc.osaka-u.ac.jp
Kohji Yanagawa
Affiliation:
Department of Mathematics, Faculty of Engineering Science Kansai University Suita, 564-8680, Japan, yanagawa@ipcku.kansai-u.ac.jp
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Abstract

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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 square-free module theory over R, and show that the Cohen-Macaulay, Buchsbaum, and Gorenstein* properties of R are topological properties of its associated cell complex.

Keywords

13F5513D25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 196 , 2009 , pp. 87 - 116
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

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