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arXiv · 2211.16109

Higher Chow cycles on a family of Kummer surfaces

Ken Sato
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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.

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Ken Sato. 2024-07-18. Higher Chow cycles on a family of Kummer surfaces. https://doi.org/10.4153/s0008414x24000415

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