Flawless 0-sequences and Hilbert functions of Cohen-Macaulay integral domains
Flawless 0-sequences and Hilbert functions of Cohen-Macaulay integral domains
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Cohen-Macaulay 积分域的完美 0 序列和希尔伯特函数
DOI：
10.1016/0022-4049(89)90085-6
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发表时间：
1989
影响因子：
0.8
通讯作者：
T. Hibi
中科院分区：
文献类型：
--
作者：
T. Hibi
设A=A0⊗A1⊗⋯是交换分次环，使得(I)A0=k是域，(Ii)A=k[A1]和(Iii)dim k A1<；∞.众所周知，形式幂级数∑∞n=0(Dim K A N)λn具有(h0+h 1λ+⋯+h SλS)(1−λ)dim A的形式，其中每个h iϵZ.我们对序列(h0，h1，…，h S)，当A是Cohen-Macaulay积分域时，称为A的h-向量。本文在总结基本结果(第一节)的基础上，研究了某些Gorenstein域的h-向量(第二节)，并找出了一些由整闭水平域产生的h-向量的例子(第三节和第四节)。
Abstract Let A= A 0⊗ A 1⊗⋯ be a commutative graded ring such that (i) A 0= k a field,(ii) A= k [A 1] and (iii) dim k A 1<∞. It is well known that the formal power series∑∞ n= 0 (dim k A n) λ n is of the form (h 0+ h 1 λ+⋯+ h s λ s)(1− λ) dim A with each h i ϵ Z. We are interested in the sequence (h 0, h 1,…, h s), called the h-vector of A, when A is a Cohen–Macaulay integral domain. In this paper, after summarizing fundamental results (Section 1), we study h-vectors of certain Gorenstein domains (Section 2) and find some examples of h-vectors arising from integrally closed level domains (Sections 3 and 4).