2008/08/31 by Ryota Okazaki, Okazaki, Ryota, Kohji Yanagawa +1
Mathematics · #13D25 #13F55 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #msc:13D25 #msc:13F55
paper · pdf · doi:10.48550/arxiv.0809.0095
22 pages
arxiv created 2008/08/31 · openalex publication_date 2008/08/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 Buchsbaum property and the Gorenstein* property of R are topological properties of its associated cell complex.