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Calabi–Yau manifolds realizing symplectically rigid monodromy tuples
Advances in Theoretical and Mathematical Physics ( IF 1.5 ) Pub Date : 2019-01-01 , DOI: 10.4310/atmp.2019.v23.n5.a3
Charles F. Doran 1 , Andreas Malmendier 2
Affiliation  

We define an iterative construction that produces a family of elliptically fibered Calabi-Yau $n$-folds with section from a family of elliptic Calabi-Yau varieties of one dimension lower. Parallel to the geometric construction, we iteratively obtain for each family with a point of maximal unipotent monodromy, normalized to be at t=0, its Picard-Fuchs operator and a closed-form expression for the period holomorphic at t=0, through a generalization of the classical Euler transform for hypergeometric functions. In particular, our construction yields one-parameter families of elliptically fibered Calabi-Yau manifolds with section whose Picard-Fuchs operators realize all symplectically rigid Calabi-Yau differential operators with three regular singular points classified by Bogner and Reiter, but also non-rigid operators with four singular points.

中文翻译:

Calabi-Yau 流形实现辛刚性的单一元组

我们定义了一个迭代构造,它产生了一个椭圆形的 Calabi-Yau $n$-folds 族,其截面来自一个低一维的椭圆形 Calabi-Yau 变种族。与几何构造平行,我们迭代地获得每个具有最大单能单性点的家族,归一化为在 t=0 处,其 Picard-Fuchs 算子和 t=0 处全纯周期的闭式表达式,通过超几何函数的经典欧拉变换的推广。特别是,我们的构造产生了椭圆纤维 Calabi-Yau 流形的单参数族,其截面的 Picard-Fuchs 算子实现了所有辛刚性的 Calabi-Yau 微分算子,具有三个由 Bogner 和 Reiter 分类的正则奇异点,但也实现了非刚性算子有四个奇异点。
更新日期:2019-01-01
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