Liaison of monomial ideals
Liaison of monomial ideals
复制标题
单项式理想的联系
DOI：
10.1112/blms/bdl008
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发表时间：
2007
影响因子：
0.9
通讯作者：
B. Ulrich
中科院分区：
文献类型：
--
作者：
C. Huneke;B. Ulrich
本文给出了判定多项式环中有限长单项式理想是否为licci的一个简单算法，即是否在完全交的链类中。该算法证明了这样的理想是否是licci并不取决于我们是否限制连接，只允许单名正则序列，或齐次正则序列，或任意正则序列。我们应用我们的结果单项式理想比较理想时，是licci与当其初始理想在一些长期秩序是licci。我们还应用Migliore和内格尔的一个思想证明了有限长度的单项理想总是glicci的，即在Gorenstein连接类的一个完整的交集。然而，我们的证明需要使用非齐次Gorenstein链接。
We give a simple algorithm to decide whether a monomial ideal of finite colength in a polynomial ring is licci, that is, in the linkage class of a complete intersection. The algorithm proves that whether or not such an ideal is licci does not depend on whether we restrict the linkage by allowing only monomial regular sequences, or homogeneous regular sequences, or arbitrary regular sequences. We apply our results on monomial ideals to compare when an ideal is licci versus when its initial ideal in some term order is licci. We also apply an idea of Migliore and Nagel to prove that monomial ideals of finite colength are always glicci, that is, in the Gorenstein linkage class of a complete intersection. However, our proof requires the use of non‐homogeneous Gorenstein links.