The transcendental part of the regulator map for K_1 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_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 Painlevé VI type differential equations.

13 pages, LaTeX. Some improvements to the previous version. We have included one example where we could explicitly solve the inhomogenous equation Dω= d_relβ. Here ωis a two form, βis a one form and D is the Picard-Fuchs operator giving the Picard-Fuchs equation of the periods

References in corpus (2)

• Sixth Painlevé Equation, Universal Elliptic Curve, and Mirror of ${\mathbf{P}}^2$
• Constructing Indecomposable Motivic Cohomology Classes on Algebraic Surfaces

Cited by in corpus (1)

• Higher Chow cycles on some K3 surfaces with involution