A new characterization of rational surface singularities
A new characterization of rational surface singularities
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有理表面奇点的新表征
DOI：
10.1007/bf01233425
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发表时间：
1990
影响因子：
3.1
通讯作者：
S. Cutkosky
中科院分区：
文献类型：
--
作者：
S. Cutkosky
设（R，m）是一个优良的二维正规局部区域.假设R/m是代数闭的。本文证明了R有有理奇点当且仅当R的任意m-准素完全理想I的完全理想12。我们给出了一个例子，证明了这个定理是假的，如果Rim不是代数闭的。相关问题已在[ZI; ZS; MS; L; G; HS]中考虑。本文是[C; C_1]和[C_2]中完备理想研究的继续。第三节给出了一个正常的例子，但不是科恩-麦考利计划，双合理地控制一个正则局部环的三维。我的主要结果是以下两个定理。
Let (R, m) be an excellent normal local domain of dimension two. Suppose that R/m is algebraically closed. In this paper it is shown that R has a rational singularity if and only if 12 is a complete ideal for any m-primary complete ideal I of R. We give an example to show that this theorem is false if Rim is not algebraically closed. Related problems have been considered in [ZI; ZS; MS; L; G; HS]. This paper is a continuation of my study of complete ideals in [C; C1] and [C2]. Section III gives an example of a normal but not Cohen-Macaulay scheme which birationally dominates a regular local ring of dimension three. My main results are the following two theorems.