Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918136785141760 |
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| author | Nemoto, Yusuke Sato, Ken |
| author_facet | Nemoto, Yusuke Sato, Ken |
| contents | 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 $\mathbb{Z}$ and generate a subgroup of $\operatorname{rank} \ge 36 \cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing the image of the transcendental regulator map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$ Nemoto, Yusuke Sato, Ken Algebraic Geometry Number Theory 14C25, 19F27 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 $\mathbb{Z}$ and generate a subgroup of $\operatorname{rank} \ge 36 \cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing the image of the transcendental regulator map. |
| title | Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$ |
| topic | Algebraic Geometry Number Theory 14C25, 19F27 |
| url | https://arxiv.org/abs/2509.05569 |