Density of algebraic points on products of curves
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912459603836928 |
|---|---|
| author | Berg, Jennifer Fu, Yu Gazaki, Evangelia Porzio, Morena Rawson, James Vogt, Isabel |
| author_facet | Berg, Jennifer Fu, Yu Gazaki, Evangelia Porzio, Morena Rawson, James Vogt, Isabel |
| contents | In this paper, we initiate the systematic study of density of algebraic points on surfaces. We give an effective asymptotic range in which the density degree set has regular behavior dictated by the index. By contrast, in small degree, the question of density is subtle and depends on the arithmetic of the curves. We give several explicit examples displaying these different behaviors, including products of genus $2$ curves with and without dense quadratic points. These results for products of curves have applications to questions about algebraic points on closely related surfaces, such as rank growth on abelian surfaces and bielliptic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Density of algebraic points on products of curves Berg, Jennifer Fu, Yu Gazaki, Evangelia Porzio, Morena Rawson, James Vogt, Isabel Number Theory Algebraic Geometry In this paper, we initiate the systematic study of density of algebraic points on surfaces. We give an effective asymptotic range in which the density degree set has regular behavior dictated by the index. By contrast, in small degree, the question of density is subtle and depends on the arithmetic of the curves. We give several explicit examples displaying these different behaviors, including products of genus $2$ curves with and without dense quadratic points. These results for products of curves have applications to questions about algebraic points on closely related surfaces, such as rank growth on abelian surfaces and bielliptic surfaces. |
| title | Density of algebraic points on products of curves |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2507.00860 |