In the author’s papers of 2013–2018, the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order were classified. For the remaining groups of small order—D₆, C₄, (C₂)², C₃, C₂, and C₁—the classification was not completed because each of these cases requires very long and difficult considerations and calculations. The case of D₆ was recently completely studied in the author’s paper of 2019. In the present paper an analogous complete classification is presented for the cyclic group C₄ of order 4.

中文翻译：

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具有辛自同构群C 4的KählerianK3曲面的简并和Picard格的分类

在作者的2013-2018年论文中，对具有高阶有限辛自同构群的KählerianK3表面的退化和Picard晶格进行了分类。对于其余的小顺序组D ₆，C ₄，（C ₂）²，C ₃，C ₂和C ₁，由于每种情况都需要很长且困难的考虑和计算，因此分类没有完成。最近在2019年的论文中对D ₆的情况进行了全面研究。在本文中，对循环群进行了类似的完全分类Ç ₄ 4阶。