Classification of degenerations and Picard lattices of Kahlerian K3 surfaces with the symplectic automorphism group (C_2)^2

TL;DR

This paper completes the classification of degenerations and Picard lattices of Kahlerian K3 surfaces with the symplectic automorphism group (C_2)^2, building on prior work for other small automorphism groups.

Contribution

It provides a complete classification for Kahlerian K3 surfaces with the automorphism group (C_2)^2, filling a gap in the understanding of degenerations for small order groups.

Findings

Complete classification of degenerations for (C_2)^2 group

Identification of Picard lattices associated with these degenerations

Extension of previous classifications to include (C_2)^2 group

Abstract

Var3: In our papers 2013--2018 we classified degenerations and Picard lattices of Kahlerian K3 surfaces with finite symplectic automorphism groups of high order. For remaining groups of small order: $D_6$, $C_4$, $(C_2)^2$, $C_3$, $C_2$ and $C_1$ it was not completely considered. Cases of $D_6$ and $C_4$ were recently completely considered in [19] and [20]. Here we consider the analogous complete classification for the group $(C_2)^2$ of the order 4.