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October 3, 2025Open Access

Construction of Higher Chow cycles on cyclic coverings of P¹ P¹

Key Points

Higher chow cycles of type (2, 1) are constructed on cyclic coverings over surfaces.
For a general member, the cycles are linearly independent over Z, generating a subgroup with rank ≥ 36φ(N).
The method involves computing the image of the transcendental regulator map, confirming independence.
The findings emphasize the significant algebraic properties of surfaces related to hypergeometric curves and their cycles.

Abstract

In this paper, we construct higher Chow cycles of type (2, 1) on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree N. We prove that for a very general member, these cycles are linearly independent over Z and generate a subgroup of rank 36 φ (N), where φ (N) is Euler's totient function, by computing the image of the transcendental regulator map.

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Cite This Study

Nemoto et al. (Sat,) studied this question.

synapsesocial.com/papers/68e034f7f0e39f13e7fa3026 https://doi.org/https://doi.org/10.48550/arxiv.2509.05569