부산대학교 도서관

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. [ABSTRACT FROM AUTHOR]