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Gauss–Manin connection in disguise: Dwork family
Journal of Differential Geometry ( IF 2.5 ) Pub Date : 2021-09-01 , DOI: 10.4310/jdg/1631124264
H. Movasati 1 , Y. Nikdelan 2
Affiliation  

We study the enhanced moduli space $\textsf{T}$ of the Calabi-Yau $n$-folds arising from Dwork family and describe a unique vector field $\textsf{R}$ in $\textsf{T}$ with certain properties with respect to the underlying Gauss-Manin connection. For $n=1,2$ we compute explicit expressions of $\textsf{R}$ and give a solution of $\textsf{R}$ in terms of quasi-modular forms.

中文翻译:

变相的高斯-马宁联系:德沃克家族

我们研究了由 Dwork 族产生的 Calabi-Yau $n$-folds 的增强模空间 $\textsf{T}$,并在 $\textsf{T}$ 中描述了一个独特的向量场 $\textsf{R}$关于底层高斯-马宁连接的属性。对于 $n=1,2$,我们计算 $\textsf{R}$ 的显式表达式,并根据准模形式给出 $\textsf{R}$ 的解。
更新日期:2021-09-01
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