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Let X be a supersingular K3 surface in characteristic 5 with Artin invariant1. Then X has a polarization that realizes X as the Fermat sextic double plane.We present a list of polarizations of X with degree 2 whose intersection numberwith this Fermat sextic polarization is less than or equal to 5, and give thedefining equations of the corresponding projective models. We also present amethod to describe birational morphisms between these projective modelsexplicitly. As a by-product, a non-projective automorphism of the Fermat sexticdouble plane is obtained.

Projective models of the supersingular K3 surface with Artin invariant 1 in characteristic 5