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- W2952497522 abstract "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 $c ge 1$, $2 le q le d$, we give an upper bound $h_{c,d,q}$ on the dimension of the unique non-vanishing homology $widetilde{H}_{q-2}(Delta;k)$ of a $d$-dimensional Buchsbaum ring $k[Delta]$ with $q$-linear resolution and codimension $c$. Also, we discuss about existence for such Buchsbaum rings with $dim_k widetilde{H}_{q-2}(Delta;k) = h$ 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." @default.
- W2952497522 created "2019-06-27" @default.
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- W2952497522 date "2003-12-27" @default.
- W2952497522 modified "2023-09-27" @default.
- W2952497522 title "Buchsbaum Stanley--Reisner rings with minimal multiplicity" @default.
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