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arXiv 1102.0518math.AG
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具有奇性的Calabi-Yau n-折叠族的Zeta函数

Zeta-Functions for Families of Calabi--Yau n-folds with Singularities

Anne Frühbis-Krüger, Shabnam Kadir

摘要:

我们考虑家庭的Calabi-Yau n-折叠包含奇异纤维和研究之间的关系发生的奇异结构和分解的局部Weil zeta函数。对于1-参数的家庭,这提供了新的见解的组合结构的强等价类中产生的Candelas -德拉Ossa -罗德里格斯-Villegas方法计算zeta函数。这也可以扩展到具有更多参数的族,如在几个示例中所探索的,其中奇异性分析提供了对当传递到奇异纤维时zeta函数分解中的程度变化的正确预测。这些观测结果为Lauder的Clemens-Schmid正合序列的简化类似物提供了第一个高维证据。

英文摘要:

We consider families of Calabi-Yau n-folds containing singular fibres and study relations between the occurring singularity structure and the decomposition of the local Weil zeta-function. For 1-parameter families, this provides new insights into the combinatorial structure of the strong equivalence classes arising in the Candelas - de la Ossa - Rodrigues-Villegas approach for computing the zeta-function. This can also be extended to families with more parameters as is explored in several examples, where the singularity analysis provides correct predictions for the changes of degree in the decomposition of the zeta-function when passing to singular fibres. These observations provide first evidence in higher dimensions for Lauder's conjectured analogue of the Clemens-Schmid exact sequence.

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