Buchsbaum Stanley–reisner Rings with Minimal Multiplicity
نویسنده
چکیده
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 H̃q−2(∆; k) of a d-dimensional Buchsbaum ring k[∆] with q-linear resolution and codimension c. Also, we discuss about existence for such Buchsbaum rings with dimk H̃q−2(∆; 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.
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