Buchsbaum Stanley--Reisner rings with minimal multiplicity

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dc.creatorTerai, Naoki
dc.creatorYoshida, Ken-ichi
dc.date2003-12-27
dc.date.accessioned2026-07-07T05:04:13Z
dc.date.available2026-07-07T05:04:13Z
dc.descriptionIn this paper, we study non-Cohen--Macaulay Buchsbaum Stanley--Reisner rings with linear free resolution. In particular, for given integers $c$, $d$, $q$ with $c \ge 1$, $2 \le q \le d$, we give an upper bound $h_{c,d,q}$ on the dimension of the unique non-vanishing homology $\widetilde{H}_{q-2}(Δ;k)$ 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 $\dim_k \widetilde{H}_{q-2}(Δ;k) = h$ for any $h$ with $0 \le h \le h_{c,d,q}$, 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.
dc.descriptionabout 25 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0312470
dc.identifierhttp://arxiv.org/abs/math/0312470
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69718
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject13F55; 13H10; 13D02
dc.titleBuchsbaum Stanley--Reisner rings with minimal multiplicity
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