摘要翻译：
以前，作者考虑并在某些情况下计算了复（法）曲面奇点上（特别是复平面上）函数芽环上两类多指标过滤的Poincare级数。第一类的过滤由曲面奇异性上的一条曲线（有几个分支）定义。另一种方法（所谓的除法滤波）是由曲面奇异性修正的例外除子的一组分量定义的。本文定义了曲面奇点上函数芽环中对应于理想或理想集的滤子，并在某些情况下计算了相应的Poincare级数。对于复平面，这个概念将上面描述的两类过滤结合在一起。
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英文标题：
《Poincare series of filtrations corresponding to ideals on surfaces》
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作者：
A. Campillo (Valladolid University, Spain), F. Delgado (Valladolid
  University, Spain), S. M. Gusein-Zade (Moscow State University, Russia)
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最新提交年份：
2008
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Earlier the authors considered and, in some cases, computed Poincare series of two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular on the complex plane). A filtration from the first class was defined by a curve (with several branches) on the surface singularity. The other one (so called divisorial filtration) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define a filtration corresponding to an ideal or to a set of ideals in the ring of germs of functions on a surface singularity and compute the corresponding Poincare series in some cases. For the complex plane this notion unites the two classes of filtrations described above.
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PDF链接：
https://arxiv.org/pdf/0803.1743