The transcendental part of the regulator map for K1 on a mirror family of K3 surfaces., by R. Pedro Luis Del Angel and Stefan Mueller-Stach

This version is a revision of a previous version of the article.

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 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 Painlev'e VI type differential equations.


R. Pedro Luis Del Angel <luis@cimat.mx>
Stefan Mueller-Stach <mueller-stach@uni-essen.de>