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ULLER-STACH Abstract We compute the transcendental part of the normal function corresponding to the Deligne class of a cycle in K1 of a mirror family of quartic K 3 surfaces. The re- sulting 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 Painlev´ e VI-type differential equations. 1. The regulator map and Picard-Fuchs equations In this paper we study the first nonclassical higher K -group K 1.X/ for a smooth com- plex projective surface X. It was conjectured by H. Esnault around 1995 that certain elements in this group can be detected in the transcendental part of the Deligne coho- mology group H 3

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