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Higher Chow cycles on a family of Kummer surfaces

Part of: Surfaces and higher-dimensional varieties Cycles and subschemes

Published online by Cambridge University Press:  02 May 2024

Ken Sato Open the ORCID record for Ken Sato [Opens in a new window]
Ken Sato*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan
*
e-mail: [email protected]
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Abstract

We construct a collection of families of higher Chow cycles of type $(2,1)$ on a two-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.

Keywords

Higher Chow cyclesregulatorPicard–Fuchs equations

MSC classification

Primary: 14C15: (Equivariant) Chow groups and rings; motives
Secondary: 14J28: $K3$ surfaces and Enriques surfaces
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 34
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The author is supported by the FMSP program by the University of Tokyo.

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