Birational extensions in dimension two and integrally closed ideals
Birational extensions in dimension two and integrally closed ideals
复制标题
二维双有理扩张和全闭理想
DOI：
10.1016/0021-8693(88)90274-8
复制
发表时间：
1988
影响因子：
0.9
通讯作者：
J. Sally
中科院分区：
文献类型：
--
作者：
C. Huneke;J. Sally
本文主要从代数的观点研究了双有理支配二维正则局部环（R，m）的二维正规局部整环（S，n）的结构.从几何的角度来看，必要条件是李普曼的文件[Lr]理性奇点，因为它遵循的早期结果之一，该文件说，S有一个理性奇点。利用初等代数技巧，我们能够恢复有关S的结构的许多信息。我们特别关注的事实（来自Lipman [Ll]和Artin [Ar]）是S必须具有最小的多重性。我们希望这种方法将有助于理解理性奇点的代数，并有助于探索二维和更高维中的许多悬而未决的问题。本文的研究框架如下。在第一节中，我们使用基本的代数技巧，如分析独立性和Zurski的主要定理来证明，例如，S有一个经常的高度1素数，如果R/m是无限的。如果S不是正则的，我们可以假设R在S中是“最大正则的”，当这种情况下，我们证明，例如，
The aim of this paper is to examine, primarily from an algebraic point of view, the structure of a 2-dimensional normal local domain (S, n) which birationally dominates a 2-dimensinal regular local ring (R, m). From the geometric point of view, the sine qua non is Lipman’s paper [Lr] on rational singularities, for it follows from one of the early results in that paper that S has a rational singularity. Using elementary algebraic techniques we are able to recover much information concerning the structure of S. We have particularly focused on the fact (from Lipman [Ll] and Artin [Ar]) that S must have minimal multiplicity. We hope this approach will aid in understanding the algebra of rational singularities and in the exploration of many open questions in dimension two and in higher dimensions. The framework of the paper is set up as follows. In the first section we use basic algebraic techniques such as analytic independence and Zariski’s Main Theorem to prove, for example, that S has a regular height 1 prime if R/m is infinite. If S is not regular, we may assume that R is “maximally regular” in S and when this is the case we show, for instance, that the