Equations for a K3 Lehmer map

TL;DR

This paper derives explicit equations for a K3 surface and its automorphism with minimal topological entropy, using a computer-aided approach based on lattice theory, Hodge structures, and automorphism reconstruction.

Contribution

It provides the first explicit equations for such a K3 surface and automorphism, combining Hodge theory with computational methods.

Findings

Explicit equations for the K3 surface and automorphism

Reconstruction of the surface from Hodge theoretic data

Application of lattice and p-adic techniques

Abstract

McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruct 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, $p$-adic lifting, elliptic fibrations and the Kneser neighbor method for integer lattices.