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The field of moduli of singular K3 surfaces
Annali di Matematica Pura ed Applicata ( IF 1.0 ) Pub Date : 2019-07-18 , DOI: 10.1007/s10231-019-00889-y Roberto Laface
中文翻译:
奇异K3曲面的模场
更新日期:2020-04-23
Annali di Matematica Pura ed Applicata ( IF 1.0 ) Pub Date : 2019-07-18 , DOI: 10.1007/s10231-019-00889-y Roberto Laface
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:
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。