A Note on Cohen-Macaulayness of Stanley-Reisner Rings with Serre's Condition (S2)
Titel:
A Note on Cohen-Macaulayness of Stanley-Reisner Rings with Serre's Condition (S2)
Auteur:
Terai, Naoki Yoshida, Ken-ichi
Verschenen in:
Communications in algebra
Paginering:
Jaargang 36 (2008) nr. 2 pagina's 464-477
Jaar:
2008-02
Inhoud:
Let Δ be a (d - 1)-dimensional simplicial complex on the vertex set V = {1, 2,…, n}. In this article, using Alexander duality, we prove that the Stanley-Reisner ring k[Δ] is Cohen-Macaulay if it satisfies Serre's condition (S2) and the multiplicity e(k[Δ]) is “sufficiently large”, that is, [image omitted]. We also prove that if e(k[Δ]) ≤ 3d - 2 and the graded Betti number β2, d+2(k[Δ]) vanishes, then the Castelnuovo-Mumford regularity reg k[Δ] is less than d.
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