论文标题
过滤在二维正常局部环上的分析扩散
Analytic spread of filtrations on two dimensional normal local rings
论文作者
论文摘要
在本文中，我们证明，麦卡达姆的古典定理是关于在noetherian本地环中理想扩散的分析性传播的，对于在二维正常出色的本地环$ r $ $ r $上的分裂过滤而言，hilbert the hilbert toletonalial the hilbert pynomial the y $ r $ r $ r $ r $具有hilbert function and the and limeal and limeal and limaine and limaine and limeal and limeal and limeal and limain and limeal and。我们通过首先研究除数的渐近性能，以$ r $ $ $ $ $ $ $ $的奇异性来证明这些定理。理想的符号能力的过滤是分区过滤的一个例子。分区过滤通常不是noe夫，在经典的理想和分区过滤效力的经典案例中给出了显着差异。
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.
