Fine behavior of symbolic powers of ideals
Fine behavior of symbolic powers of ideals
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理想象征力量的优良行为
DOI：
10.1215/ijm/1258735331
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发表时间：
2007
影响因子：
0.6
通讯作者：
C. Huneke
中科院分区：
文献类型：
--
作者：
M. Hochster;C. Huneke
Ein，Lazarsfeld和Smith在2001年发现了正则环中理想的符号幂和通常幂的一个基本性质，后来Hochster和Huneke在2002年推广了这个性质。本文给出了理想正则环的商为F-纯型或F-纯型时更好结果的进一步推广。我们的方法也解释了Eisenbud和Mazur关于进化存在的一个猜想。所使用的方法是从紧封闭和归约到正特征。这篇文章是为了欣赏菲尔·格里菲斯对交换代数的许多贡献。
A fundamental property connecting the symbolic powers and the usual powers of ideals in regular rings was discovered by Ein, Lazarsfeld, and Smith in 2001, and later extended by Hochster and Huneke in 2002. In this paper we give further generalizations which give better results in case the quotient of the regular ring by the ideal is F-pure or F-pure type. Our methods also give insight into a conjecture of Eisenbud and Mazur concerning the existence of evolutions. The methods used come from tight closure and reduction to positive characteristic. This paper is written in appreciation of the many contributions of Phil Griffith to commutative algebra.