Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
复制标题
Calabi-Yau 三重的 Picard-Fuchs 微分方程的单向性
DOI：
10.1515/crelle.2008.021
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发表时间：
2006
影响因子：
2.8
通讯作者：
C. Erdenberger
中科院分区：
文献类型：
--
作者：
Yao;Yifan Yang;N. Yui;C. Erdenberger
本文研究了一类单参数Calabi-Yau三重函数族的Picard-Fuchs微分方程的单值性。我们的结果表明，在超几何的情况下，矩阵表示的monodromy相对于Frobenius基地可以表示的几何不变量的基础Calabi-Yau三倍。本文还对其它Calabi-Yau三重函数族的情况进行了数值验证。进一步，我们发现在适当的基变换下，单值群包含在Sp（4，n）的某些有限指数同余子群中，且其水平与Calabi-Yau三重几何不变量有关.
Abstract In this paper we are concerned with the monodromy of Picard-Fuchs differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of monodromy relative to the Frobenius bases can be expressed in terms of the geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon is also verified numerically for other families of Calabi-Yau threefolds in the paper. Furthermore, we discover that under a suitable change of bases the monodromy groups are contained in certain congruence subgroups of Sp(4, ℤ) of finite index and whose levels are related to the geometric invariants of the Calabi-Yau threefolds.