K3 surfaces with a symplectic automorphism of order 4

Given , a K3 surface admitting a symplectic automorphism of order 4, we describe the isometry on . Having called and , respectively, the minimal resolutions of the quotient surfaces and , we also describe the maps induced in cohomology by the rational quotient maps and : With this knowledge, we are able to give a lattice‐theoretic characterization of , and find the relation between the Néron–Severi lattices of and in the projective case. We also produce three different projective models for and , each associated to a different polarization of degree 4 on .