We give a computable lower bound for the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether–Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups.

中文翻译：

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四次曲面的周期分离

我们给出了在代数数上定义的给定四次曲面的两个不同周期之间的距离的可计算下界。主要成分是确定 Noether-Lefschetz 基因座成分的高度界限。这使得研究四次曲面周期的丢番图性质并验证其皮卡德群的部分数值计算成为可能。