ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS
ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS
复制标题
DOI：
10.1017/nmj.2022.35
复制
发表时间：
2022-03
影响因子：
0.8
通讯作者：
S. Cutkosky
中科院分区：
文献类型：
--
作者：
S. Cutkosky
本文证明了McAdam关于Noether局部环中理想的解析展开的经典定理对于二维正规优良局部环R上的除滤仍然成立，且R上除滤的纤维锥的Hilbert多项式有一个Hilbert函数，它是一个线性多项式与一个有界函数之和。我们首先研究了R的谱的奇点分解上因子的渐近性质，证明了这些定理。理想的符号幂的过滤是除法过滤的一个例子。除滤通常不是诺特的，在理想幂滤和除滤的经典情况下给出了显著的区别。
Abstract In this paper, we prove that a classical theorem by McAdam about the analytic spread of an ideal in a Noetherian local ring continues to be true for divisorial filtrations on a two-dimensional normal excellent local ring R, and that the Hilbert polynomial of the fiber cone of a divisorial filtration on R has a Hilbert function which is the sum of a linear polynomial and a bounded function. We prove these theorems by first studying asymptotic properties of divisors on a resolution of singularities of the spectrum of R. The filtration of the symbolic powers of an ideal is an example of a divisorial filtration. Divisorial filtrations are often not Noetherian, giving a significant difference in the classical case of filtrations of powers of ideals and divisorial filtrations.