We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.

中文翻译：

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从虚拟校正到 Drell-Yan 散射产生的 K3 表面的算术和几何

我们研究了 K3 表面，它出现在对 Drell-Yan 散射的双环混合电弱量子色动力学虚拟校正中。给出了几何皮卡德格的详细分析，以两种独立的方式计算其秩和判别式：首先使用表面上的显式除数，然后使用显式椭圆纤维化。我们还详细研究了表面的椭圆纤维，并使用它们来提供明确的 Shioda--Inose 结构。此外，我们指出了我们结果的物理相关性。