Containment counterexamples for ideals of various configurations of points in PN
Containment counterexamples for ideals of various configurations of points in PN
复制标题
PN 中各种点配置理想的包含反例
DOI：
10.1016/j.jpaa.2014.05.034
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发表时间：
2013
影响因子：
0.8
通讯作者：
A. Seceleanu
中科院分区：
文献类型：
--
作者：
B. Harbourne;A. Seceleanu
当I是域K上投射N-空间PN中有限点集的根齐性理想时，证明了对所有r≥ 1，I（rN − N+ 1）应包含在Ir中。最近的反例表明，当N= r= 2时，这可能失败。我们研究由此产生的理想的性质。我们还表明，故障发生无穷多个r在每个特征p> 2时，N= 2，我们发现额外的正特征故障时，N> 2。
When I is the radical homogeneous ideal of a finite set of points in projective N-space, P N, over a field K, it has been conjectured that I (r N− N+ 1) should be contained in I r for all r≥ 1. Recent counterexamples show that this can fail when N= r= 2. We study properties of the resulting ideals. We also show that failures occur for infinitely many r in every characteristic p> 2 when N= 2, and we find additional positive characteristic failures when N> 2.