The field of moduli of singular K3 surfaces

被引：0

作者：

Roberto Laface

机构：

[1] Technische Universität München,

来源：

Annali di Matematica Pura ed Applicata (1923 -) | 2020年 / 199卷

关键词：

K3 surfaces; Abelian surfaces; Elliptic curves; Complex multiplication; Class field theory; Field of moduli; 14J28; 14K15; 14K22;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We study the field of moduli of singular K3 surfaces. We discuss both the field of moduli over the CM field and over Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathbb {Q}}}$$\end{document}. 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.

引用

页码：509 / 531

页数：22

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