학술논문
On the stable Harbourne conjecture for ideals defining space monomial curves
Document Type
Working Paper
Author
Source
Proc. Amer. Math. Soc., electronically published on January 24, 2022
Subject
Language
Abstract
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.