Cohen-Macaulay local rings of maximal embedding dimension
Cohen-Macaulay local rings of maximal embedding dimension
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最大嵌入维数的 Cohen-Macaulay 局部环
DOI：
10.1016/0021-8693(79)90331-4
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发表时间：
1979
影响因子：
0.9
通讯作者：
J. Sally
中科院分区：
文献类型：
--
作者：
J. Sally
设（R，m）是重数为e的d维局部Cohen-Macaulay环.若v表示R的嵌入维数，则v< e+ d~ 1，[1].如果a= d或d-11，R的大部分结构，根据希尔伯特函数，贝蒂数等测量设备，完全由e决定。我们证明了对于嵌入维数为71= e-kd-1的d维局部Cohen-Macaulay环和嵌入维数为e-Td-2的d维局部Gorenstein环也是如此。对这些环的研究开始于[161]和[17]，其中给出了相关分次环的性质。本文中的一些结果的灵感来自Wahl的论文[18]，该论文给出了定义有理曲面奇异性和某些椭圆奇异性的方程。在这些奇点处的局部环是这里讨论的环的例子。我想感谢J. Wahl建议在[16]和[171]中开始的调查可以进一步进行。
Let (R, m) be a d-dimensional local Cohen-Macaulay ring of multiplicity e. If v denotes the embedding dimension of R, v< e+ d~ 1,[l]. If a= d or d-1 1 much of the structure of R, in terms of such measuring devices as the Hilbert function, Betti numbers etc., is completely determined by e. We show here that the same is true for d-dimensional local Cohen-Macaulay rings of embedding dimension 71= e-kd-1 and d-dimensional local Gorenstein rings of embedding dimension e T d-2. An investigation of these rings was begun [161 and [17] where properties of the associated graded rings were given. Inspiration for some of the results in this paper comes from the paper [18] of Wahl which gives equations defining rational surface singularities and certain elliptic singularities. The local rings at these singularities are examples of the rings under discussion here. I wish to thank J. Wahl for suggesting that the investigations begun in [16] and [I71 could be carried further.