The transcendental part of the regulator map for K_1 on a mirror family of K3 surfaces

Details The transcendental part of the regulator map for K_1 on a mirror family of K3 surfaces The transcendental part of the regulator map for K_1 on a mirror family of K3 surfaces

2000-08-28

arxiv.org/abs/math/0008207v4

Mathematics

Algebraic Geometry

13 pages, LaTeX. Some improvements to the previous version. We have included one example where we could explicitly solve the i

Scientific paper

We compute the transcendental part of the normal function corresponding to the Deligne class of a cycle in K_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 equation are related to Painlev\'e VI type differential equations.

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