A stable version of Harbourne's Conjecture and the containment problem for space monomial curves
A stable version of Harbourne's Conjecture and the containment problem for space monomial curves
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哈伯恩猜想的稳定版本和空间单项式曲线的包含问题
DOI：
10.1016/j.jpaa.2020.106435
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发表时间：
2018
影响因子：
0.8
通讯作者：
Eloísa Grifo
中科院分区：
文献类型：
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作者：
Eloísa Grifo
多项式环中根理想I的符号幂I (n)是由I定义的在n阶以内消失的函数组成的。它们不一定与普通代数幂I n一致，但是比较这两个概念是很自然的。遏制问题包括确定I (n)≥m的n和m的值。当I是正环中高度为2的理想时，I(3)≥≥I 2，但我们证明，对于空间单项式曲线（t a, t b, t c）的定义理想，该约束条件成立。更一般地说，给定一个大高度h的根式理想I，而Harbourne所推测的I (h n−h+ 1)≥≥n的约束并不一定对所有n成立，我们给出了保证≥n≤0时I (h n−h+ 1)≥n的充分条件。
The symbolic powers I (n) of a radical ideal I in a polynomial ring consist of the functions that vanish up to order n in the variety defined by I. These do not necessarily coincide with the ordinary algebraic powers I n, but it is natural to compare the two notions. The containment problem consists of determining the values of n and m for which I (n)⊆ I m holds. When I is an ideal of height 2 in a regular ring, I (3)⊆ I 2 may fail, but we show that this containment does hold for the defining ideal of the space monomial curves (t a, t b, t c). More generally, given a radical ideal I of big height h, while the containment I (h n− h+ 1)⊆ I n conjectured by Harbourne does not necessarily hold for all n, we give sufficient conditions to guarantee I (h n− h+ 1)⊆ I n for n≫ 0.
余维两个科恩-麦考利理想的符号幂
影响因子：
0.7
作者：
Cooper, Susan;Fatabbi, Giuliana;Guardo, Elena;Lorenzini, Anna;Migliore, Juan;Nagel, Uwe;Seceleanu, Alexandra;Szpond, Justyna;Tuyl, Adam Van
通讯作者：
Tuyl, Adam Van