On the duality between the heterotic string and F-theory in 8 dimensions

In this note we compare the moduli spaces of the heterotic string compactified on a two-torus and F-theory compactified on an elliptic K3 surface for the case of an unbroken E8 × E8 gauge group. The explicit map relating the deformation parameters α and β of the F-theory K3 surface to the moduli T and U of the heterotic torus is found using the close relationship between the K3 discriminant and the discriminant of the Calabi-Yau-threefold X1,1,2,8,12(24) in the limit of a large base P1.