Given , a K3 surface admitting a symplectic automorphism of order 4, we describe the isometry on . Having called and , respectively, the minimal resolutions of the quotient surfaces and , we also describe the maps induced in cohomology by the rational quotient maps and : With this knowledge, we are able to give a lattice‐theoretic characterization of , and find the relation between the Néron–Severi lattices of and in the projective case. We also produce three different projective models for and , each associated to a different polarization of degree 4 on .

中文翻译：

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具有 4 阶辛自同构的 K3 曲面

给定 ，一个 K3 曲面承认 4 阶辛自同构，我们描述 上的等距。分别称 和 为商曲面 和 的最小分辨率，我们还描述了由有理商映射 和 导出的上同调映射：有了这些知识，我们能够给出 的晶格理论表征，并找到关系在射影情况下 和 的 Néron-Severi 晶格之间。我们还为 和 生成了三种不同的投影模型，每个模型都与 上的 4 阶不同极化相关。