Equations for a K3 Lehmer map

Abstract

C. T. McMullen proved the existence of a K3 surface with an automorphism of entropy given by the logarithm of Lehmer’s number, which is the minimum possible among automorphisms of complex surfaces. We reconstruct equations for the surface and its automorphism from the Hodge theoretic model provided by McMullen. The approach is computer aided and relies on finite non-symplectic automorphisms, p p -adic lifting, elliptic fibrations and the Kneser neighbor method for Z \mathbb {Z} -lattices. It can be applied to reconstruct any automorphism of an elliptic K3 surface from its action on the Neron-Severi lattice.