The transcendental part of the regulator map forK1 on a mirror family of K3-surfaces

Abstract

We compute the transcendental part of the normal function corresponding to the Deligne class of a cycle in $K\sb 1$ of a mirror family of quartic $K3$ surfaces. The resulting multivalued function does not satisfy the hypergeometric differential equation of the periods, and we conclude that the cycle is indecomposable for most points in the mirror family. The occurring inhomogenous Picard-Fuchs equations are related to Painlevé VI-type differential equations.