Construction of higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$, Part II
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918371459596288 |
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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 family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very general member, these cycles generate a subgroup of the indecomposable part of $\operatorname{rank} \ge n\cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing their images under the transcendental regulator map. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_04888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$, Part II Nemoto, Yusuke Sato, Ken Algebraic Geometry Number Theory 14C25, 19F27, 33C65 In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very general member, these cycles generate a subgroup of the indecomposable part of $\operatorname{rank} \ge n\cdot φ(N)$, where $φ(N)$ is Euler's totient function, by computing their images under the transcendental regulator map. |
| title | Construction of higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$, Part II |
| topic | Algebraic Geometry Number Theory 14C25, 19F27, 33C65 |
| url | https://arxiv.org/abs/2603.04888 |