Poincaré series of curves on rational surface singularities
Poincaré series of curves on rational surface singularities
复制标题
有理曲面奇点上的庞加莱级数曲线
DOI：
10.4171/cmh/6
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
S. Gusein
中科院分区：
文献类型：
--
作者：
A. Campillo;Félix Delgado de la Mata;S. Gusein
对于嵌入在有理曲面奇点中的可约曲线奇点，计算了庞加莱级数。这里的庞加莱级数是由多指标过滤定义的局部环上定义的函数的命令的分支曲线。计算方法基于函数环投影化上关于欧拉特征线的积分概念（概念类似于motivic积分的概念并受到其启发）。对于E_8曲面的奇异性，Poincare级数与相应链环的亚历山大多项式是一致的
For a reducible curve singularity embedded in a rational surface singularity the Poincare series is computed. Here the Poincare series is defined by the multi-index filtration on the local ring defined by orders of a function on the branches of the curve. The method of the computations is based on the notion of the integral with respect to the Euler characteristic over the projectivization of the ring of functions (notion similar to, and inspired by, the notion of motivic integration). For the case of the E_8 surface singularity it appears that the Poincare series coincides with the Alexander polynomial of the corresponding link