论文标题
在稳定的Harbourne猜想中，定义空间曲线的理想
On the stable Harbourne conjecture for ideals defining space monomial curves
论文作者
论文摘要
对于理想的$ \ Mathfrak {p} $ in $ k [x，y，z] $定义空间单曲线，我们表明$ \ m athfrak {p}^{（2 n -1）} \ subseteq \ subseteq \ mathfrak {m} mathfrak {m} {m}最大理想$（x，y，z）$。此外，确定了最小的这样的$ n $。事实证明，由于Grifo，Huneke和Mukundan引起的主张有一个反例，其中指出$ \ Mathfrak {p}^{（3）} \ subseteq \ subseteq \ Mathfrak {M} \ Mathfrak {Mathfrak {p}^2 $ k $是特征性的领域，是一个特征性的领域，不是$ 3 $ 3 $ 3 $; 3 $ 3 $;但是，稳定的Harbourne猜想对太空单曲线所声称的构想保持不变。
For the ideal $\mathfrak{p}$ in $k[x, y, z]$ defining a space monomial curve, we show that $\mathfrak{p}^{(2 n - 1)} \subseteq \mathfrak{m} \mathfrak{p}^{n}$ for some positive integer $n$, where $\mathfrak{m}$ is the maximal ideal $(x, y, z)$. Moreover, the smallest such $n$ is determined. It turns out that there is a counterexample to a claim due to Grifo, Huneke, and Mukundan, which states that $\mathfrak{p}^{(3)} \subseteq \mathfrak{m} \mathfrak{p}^2$ if $k$ is a field of characteristic not $3$; however, the stable Harbourne conjecture holds for space monomial curves as they claimed.
