镜像五次Calabi-Yau簇上的模型函数
Modular-type functions attached to mirror quintic Calabi-Yau varieties
摘要：
本文研究了一类附加在单参数Calabi-Yau簇族周期上的模型函数的微分代数，该簇族与泛五次三重簇族是镜像对偶的.这样的代数是由7个函数生成的满足功能和微分方程并行的模块函数方程的经典爱森斯坦级数和拉马努金微分方程。我们的结果是第一个例子的自同构型函数附加到品种的周期域不是厄米对称的。它是70年代左右Griffiths关于极化Hodge结构模的自守函数的存在性问题的重新表述和实现。
英文摘要：
In this article we study a differential algebra of modular-type functions attached to the periods of a one parameter family of Calabi-Yau varieties which is mirror dual to the universal family of quintic threefolds. Such an algebra is generated by seven functions satisfying functional and differential equations in parallel to the modular functional equations of classical Eisenstein series and the Ramanujan differential equation. Our result is the first example of automorphic-type functions attached to varieties whose period domain is not Hermitian symmetric. It is a reformulation and realization of a problem of Griffiths around seventies on the existence of automorphic functions for the moduli of polarized Hodge structures.
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