K3 surfaces and sphere packings

Abstract

We determine the structure of the Mordell-Weil lattice, Néion-Severi lattice and the lattice of transcendental cycles for certain elliptic K3 surfaces. We find that such questions from algebraic geometry are closely related to the sphere packing problem, and a key ingredient is the use of the sphere packing bounds in establishing geometric results. © 2008 The Mathematical Society of Japan.