Construction of higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$, Part II
Abstract
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.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Advanced Mathematical Identities
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 March 2026
- Language
- EN
- Document type
- Preprint