Uniformization of some weight 3 variations of Hodge structure, Anosov representations, and Lyapunov exponents
Uniformization of some weight 3 variations of Hodge structure, Anosov representations, and Lyapunov exponents
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Hodge 结构、Anosov 表示和 Lyapunov 指数的一些权重 3 变体的均匀化
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Simion Filip
中科院分区：
文献类型：
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作者：
Simion Filip
我们针对 Hodge 结构 (VHS) 的某些权重 3 变化开发了一类均匀化。 VHS 的解析性质用于建立 Eskin、Kontsevich、M"oller 和 Zorich 对 Lyapunov 指数的猜想。此外，我们证明单调表示是对数阿诺索夫（log-Anosov），这是一种对 VHS 具有许多全局后果的动力学性质。我们为 VHS 建立了强大的 Torelli 定理并描述了适当的不连续域。此外，我们对满足我们的超几何微分方程进行了分类。我们获得了几个多参数方程组，其中包括镜像五次方程以及 Doran-Morgan 和 Brav-Thomas 的其他六个薄例。
We develop a class of uniformizations for certain weight 3 variations of Hodge structure (VHS). The analytic properties of the VHS are used to establish a conjecture of Eskin, Kontsevich, M"oller, and Zorich on Lyapunov exponents. Additionally, we prove that the monodromy representations are log-Anosov, a dynamical property that has a number of global consequences for the VHS. We establish a strong Torelli theorem for the VHS and describe appropriate domains of discontinuity. Additionally, we classify the hypergeometric differential equations that satisfy our assumptions. We obtain several multi-parameter families of equations, which include the mirror quintic as well as the six other thin cases of Doran--Morgan and Brav--Thomas.