二十面体不变量与由$K3$曲面周期构造类域
Icosahedral invariants and a construction of class fields via periods of $K3$ surfaces
摘要：
在复乘理论中，构造CM域上的类域是一个重要的问题。在本文中，我们考虑明确的$K3$曲面参数化的克莱因二十面体不变量。通过$K3$曲面的周期和Shioda-Inose结构，二十面体不变量的特殊值在四次CM域上生成类域。此外，我们通过$K3$曲面的周期给出了最简单情况下Shimura簇的正则模型的显式表达式。
英文摘要：
In the theory of complex multiplication, it is important to construct class fields over CM fields. In this paper, we consider explicit $K3$ surfaces parametrized by Klein's icosahedral invariants. Via the periods and the Shioda-Inose structures of $K3$ surfaces, the special values of icosahedral invariants generate class fields over quartic CM fields. Moreover, we give an explicit expression of the canonical model of the Shimura variety for the simplest case via the periods of $K3$ surfaces.
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