Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group C4

Abstract

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.