Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
Symbolic powers versus regular powers of ideals of general points in P^1 x P^1
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P^1 x P^1 中一般点的理想的符号幂与常规幂
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Tuyl
中科院分区：
文献类型：
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作者：
E. Guardo;B. Harbourne;A. Tuyl
最近，Ein-Lazarsfeld-Smith和Hochster-Huneke提出了一个问题，即理想的象征性权力包含在理想的给定普通权力中。Bocci-Harbourne开发了解决这个问题的方法，其中涉及理想符号权力的渐近数值特征。迄今为止所做的大部分工作都是为了定义射影空间的0维子格式。这里我们主要讨论由${f P}^3$中的线的并集给出的某些子方案，这些子方案也可以看作${f P}^1乘以{f P}^1$中的点。我们还得到了由Hochster和Li-Swanson研究的密切相关的问题的结果，即确定理想的每个符号幂是普通幂的情况。
Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci-Harbourne developed methods to address this problem, which involve asymptotic numerical characters of symbolic powers of the ideals. Most of the work done up to now has been done for ideals defining 0-dimensional subschemes of projective space. Here we focus on certain subschemes given by a union of lines in ${f P}^3$ which can also be viewed as points in ${f P}^1 imes {f P}^1$. We also obtain results on the closely related problem, studied by Hochster and by Li-Swanson, of determining situations for which each symbolic power of an ideal is an ordinary power.