2003/12/27 by Naoki Terai, Ken-ichi Yoshida, Terai, Naoki +1
Mathematics · #13D02 #13F55 #13H10 #Advanced Topics in Algebra #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.CO #msc:13D02 #msc:13F55 #msc:13H10
paper · pdf · doi:10.48550/arxiv.math/0312470
about 25 pages, LaTeX
arxiv created 2003/12/27 · openalex publication_date 2003/12/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study non-Cohen--Macaulay Buchsbaum Stanley--Reisner rings with linear free resolution. In particular, for given integers c, d, q with c ≥ 1, 2 ≤ q ≤ d, we give an upper bound hc,d,q on the dimension of the unique non-vanishing homology \widetildeHq-2(Δ;k) of a d-dimensional Buchsbaum ring k[Δ] with q-linear resolution and codimension c. Also, we discuss about existence for such Buchsbaum rings with dimk \widetildeHq-2(Δ;k) = h for any h with 0 ≤ h ≤ hc,d,q, and prove an existence theorem in the case of q=d=3 using the notion of Cohen--Macaulay linear cover. On the other hand, we introduce the notion of Buchsbaum Stanley--Reisner rings with minimal multiplicity of type q, which extends the notion of Buchsbaum rings with minimal multiplicity defined by Goto. As an application, we give many examples of Buchsbaum Stanley--Reisner rings with q-linear resolution.