摘要翻译：
对于$\mathbb{C}[x,y]$中的理想，可以关联一个拓扑zeta函数。这是与一个多项式相关的拓扑zeta函数的推广。但在这种情况下，我们使用理想的原则化，而不是曲线的嵌入分辨率。本文将研究关于此zeta函数极点的两个问题。首先，我们将给出一个判断候选极点是否为极点的判据。原来，只要看一下原理的相交图，再加上异常曲线的数值数据，我们就可以马上知道这一点。之后，我们将完整地描述一组有理数，这些有理数可以作为拓扑zeta函数的极点出现，该函数与维数2中的理想相关联。同样的结果也适用于相关的zeta函数，例如motivic zeta函数。
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英文标题：
《Poles of the topological zeta function associated to an ideal in
  dimension two》
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作者：
Lise Van Proeyen and Willem Veys
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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：
  To an ideal in $\mathbb{C}[x,y]$ one can associate a topological zeta function. This is an extension of the topological zeta function associated to one polynomial. But in this case we use a principalization of the ideal instead of an embedded resolution of the curve.   In this paper we will study two questions about the poles of this zeta function. First, we will give a criterion to determine whether or not a candidate pole is a pole. It turns out that we can know this immediately by looking at the intersection diagram of the principalization, together with the numerical data of the exceptional curves. Afterwards we will completely describe the set of rational numbers that can occur as poles of a topological zeta function associated to an ideal in dimension two. The same results are valid for related zeta functions, as for instance the motivic zeta function.
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PDF链接：
https://arxiv.org/pdf/0711.3134