摘要翻译：
一个固定射影变种的所有周变种的欧拉特征可以收集在一个形式幂级数中，称为欧拉-周级数。当Picard群是有限生成的自由阿贝尔群时，该级数与Hilbert级数一致。寻找这个系列对于哪些变种是合理的是一个有趣的公开问题。对几种情况进行了计算，怀疑该级数对于P^2在一般位置九个点的爆破是不合理的。将这个系列扩展到周动机，并问这个系列是合理的还是寻找一个反例，这是非常自然的。在本文中，我们对级数进行了推广，并通过一个例子说明了级数是非理性的。这就打开了欧拉-周级数的几何意义的问题。
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英文标题：
《Irrationality of motivic series of Chow varieties》
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作者：
E. Javier Elizondo and Shun-Ichi Kimura
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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：
  The Euler characteristic of all the Chow varieties, of a fixed projective variety, can be collected in a formal power series called the Euler-Chow series. This series coincides with the Hilbert series when the Picard group is a finite generated free abelian group. It is an interesting open problem to find for which varieties this series is rational. A few cases have been computed, and it is suspected that the series is not rational for the blow up of P^2 at nine points in general position.   It is very natural to extend this series to Chow motives and ask the question if the series is rational or to find a counterexample. In this short paper we generalized the series and show by an example that the series is not rational. This opens the question of what is the geometrical meaning of the Euler-Chow series.
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PDF链接：
https://arxiv.org/pdf/0706.0931