Dualizing complex of a toric face ring
arXiv:0809.0095
Abstract
A "toric face ring", which generalizes both Stanley-Reisner rings and affine semigroup rings, is studied by Bruns, Roemer and their coauthors recently. In this paper, under the "normality" assumption, we describe a dualizing complex of a toric face ring in a very concise way. Since is not a graded ring in general, the proof is not straightforward. We also develop the squarefree module theory over , and show that the Buchsbaum property and the Gorenstein* property of are topological properties of its associated cell complex.
22 pages