Classification of Degenerations of Codimension ${\le }\,5$ and Their Picard Lattices for Kählerian K3 Surfaces with the Symplectic Automorphism Group $(C_2)^2$

In our papers of 2013–2018, we classified degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order. For the remaining groups of small order—$D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$, and $C_1$—the classification was not completed, because each of these cases requires very long and difficult considerations and calculations. The cases of $D_6$ and $C_4$ have been recently completely analyzed. Here we consider an analogous complete classification for the group $(C_2)^2$ of order $4$. We restrict ourselves to degenerations of codimension ${\le }\,5$. This group also has degenerations of codimension $6$ and $7$, which will be classified in a future paper.