Higher Chow cycles on a family of Kummer surfaces

Abstract

We construct a collection of families of higher Chow cycles of type $(2,1)$ on a 2-dimensional family of Kummer surfaces, and prove that for a very general member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of the higher Chow group. Construction of the cycles uses a finite group action on the family, and the proof of their linear independence uses Picard-Fuchs differential operators.

28 pages, 5 figures. To appear in Canad. J. Math

Cited by in corpus (1)

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