Geodesic
Classification of Degenerations of Codimension ${\le }\,5$ and Their Picard Lattices for K\"ahlerian K3 Surfaces with the Symplectic Automorphism Group $(C_2)^2$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 189-242

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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. 
@article{TM_2023_320_a8,
     author = {Viacheslav V. Nikulin},
     title = {Classification of {Degenerations} of {Codimension} ${\le }\,5$ and {Their} {Picard} {Lattices} for {K\"ahlerian} {K3} {Surfaces} with the {Symplectic} {Automorphism} {Group} $(C_2)^2$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {189--242},
     publisher = {mathdoc},
     volume = {320},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_320_a8/}
}
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Viacheslav V. Nikulin. Classification of Degenerations of Codimension ${\le }\,5$ and Their Picard Lattices for K\"ahlerian K3 Surfaces with the Symplectic Automorphism Group $(C_2)^2$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 189-242. http://geodesic.mathdoc.fr/item/TM_2023_320_a8/