We study the field of moduli of singular K3 surfaces. We discuss both the field of moduli over the CM field and over \({{\mathbb {Q}}}\). As a by-product, we show non-finiteness of isomorphism classes of singular K3 surfaces with field of moduli of bounded degree. Finally, we provide an explicit description of the field of moduli in terms of the 2-torsion of the Galois group of the ring class field over which the K3 surface is defined.

中文翻译：

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奇异K3曲面的模场

我们研究奇异K3曲面的模场。我们同时讨论CM字段和\（{{\ mathbb {Q}}} \）上的模场。作为副产品，我们显示了奇异K3曲面的同构类的无限性，其模场为有界度。最后，我们根据定义K3曲面的环类场的Galois组的2扭转来对模场进行明确描述。