Abstract

We report on a new approach, as well as some related experiments, to construct families of K3 surfaces having real or complex multiplication. The approach is based on an explicit description of the transcendental part of the cohomology in a topological way, using topological tori. Fundamental ideas include considering the period space of marked K3 surfaces, determining the periods by numerical integration, as well as tracing the modular curve by a numerical continuation method.

中文翻译：

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通过周期积分在 K3 曲面上进行实数和复数乘法

摘要

我们报告了一种新方法以及一些相关实验，以构建具有实数或复数乘法的K 3 曲面族。该方法基于使用拓扑环以拓扑方式明确描述上同调的超越部分。基本思想包括考虑标记K 3 曲面的周期空间，通过数值积分确定周期，以及通过数值延拓法跟踪模曲线。