Higher Chow cycles on K3 surfaces attached to plane quartics

2024/08/17 by Ken Sato, Sato, Ken
Computer Science · Mathematics · #14C15 #14J28 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2408.09102

openalex publication_date 2024/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give an explicit construction of higher Chow cycles of type (2,1) on K3 surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the quartics. We prove that the higher Chow cycles generate a rank 2 subgroup in the indecomposable part of the higher Chow group for very general members, by using a specialization argument and an explicit computation of the regulator map.

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