Elliptic constant cycle curves on Kummer surfaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916782497857536 |
|---|---|
| author | Huang, Jiexiang |
| author_facet | Huang, Jiexiang |
| contents | The order of a constant cycle curve $C \subset X$ on a K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class $Δ_C$ in the Chow group $\mathrm{CH}^2(X \times C)$. In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian $J_{\mathrm{tr}}^3(X \times C)$. As a consequence, every $n \in \mathbb{N}$ can be realized as the order of a constant cycle curve on a K3 surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic constant cycle curves on Kummer surfaces Huang, Jiexiang Algebraic Geometry The order of a constant cycle curve $C \subset X$ on a K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class $Δ_C$ in the Chow group $\mathrm{CH}^2(X \times C)$. In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian $J_{\mathrm{tr}}^3(X \times C)$. As a consequence, every $n \in \mathbb{N}$ can be realized as the order of a constant cycle curve on a K3 surface. |
| title | Elliptic constant cycle curves on Kummer surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2506.06260 |