Cohen-Macaulayness of large powers of Stanley-Reisner ideals
Cohen-Macaulayness of large powers of Stanley-Reisner ideals
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DOI：
10.1016/j.aim.2011.10.004
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发表时间：
2010-09
期刊：
影响因子：
--
通讯作者：
N. Terai;N. Trung
中科院分区：
文献类型：
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作者：
N. Terai;N. Trung
我们证明了对于m-⩾3，Stanley-Reisner理想的符号幂I-Δ(M)是Cohen-Macaulay当且仅当单纯复形Δ是拟阵。类似地，当且仅当IΔ是完全交时，当且仅当I⩾是完全交时，对于某个mΔ3，平方幂I是错失的科恩-麦考利。这些结果解决了关于Stanley-Reisner理想的普通幂和符号幂的Cohen-Macaulay性的几个悬而未决的问题。此外，它们对刻面理想和覆盖理想的象征幂的Cohen-Macaulay性有有趣的结果。
We prove that for m⩾3, the symbolic power IΔ(m)of a Stanley–Reisner ideal is Cohen–Macaulay if and only if the simplicial complex Δ is a matroid. Similarly, the ordinary power IΔmis Cohen–Macaulay for some m⩾3 if and only if IΔis a complete intersection. These results solve several open questions on the Cohen–Macaulayness of ordinary and symbolic powers of Stanley–Reisner ideals. Moreover, they have interesting consequences on the Cohen–Macaulayness of symbolic powers of facet ideals and cover ideals.