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摘要翻译：
在以往的文献中，计算了有理曲面奇点上函数芽环上的一些（多指标）过滤的Poincare级数。这些庞加莱级数被写成某些分数幂级数的整数部分，没有给出对其的解释。本文证明，对于简单的变量变化，这些分数幂级数是曲面奇点的普适阿贝尔覆盖上函数芽环上过滤的等变Poincare级数的专门化。我们计算这些等变Poincare级数。
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英文标题：
《Universal abelian covers of rational surface singularities and
multi-index filtrations》
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作者：
A. Campillo, F. Delgado, S.M. Gusein-Zade
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最新提交年份：
2007
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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：
In previous papers, there were computed the Poincare series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincare series were written as the integer parts of certain fractional power series, an interpretation of whom was not given. Here we show that, up to a simple change of variables, these fractional power series are specializations of the equivariant Poincare series for filtrations on the ring of germs of functions on the universal abelian cover of the surface singularity. We compute these equivariant Poincare series.
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PDF链接：
https://arxiv.org/pdf/0706.4062
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