Rational points on K3 surfaces of degree 2
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_ | 1866909847994236928 |
|---|---|
| author | Martínez-Marín, Júlia |
| author_facet | Martínez-Marín, Júlia |
| contents | A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree of such an extension. Moreover, using ideas of van Luijk and a surface constructed by Elsenhans and Jahnel, we give an explicit family of K3 surfaces of degree 2 defined over $\mathbb{Q}$ with geometric Picard number 1 and infinitely many $\mathbb{Q}$-rational points that is Zariski dense in the moduli space of K3 surfaces of degree 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13262 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational points on K3 surfaces of degree 2 Martínez-Marín, Júlia Number Theory Algebraic Geometry A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree of such an extension. Moreover, using ideas of van Luijk and a surface constructed by Elsenhans and Jahnel, we give an explicit family of K3 surfaces of degree 2 defined over $\mathbb{Q}$ with geometric Picard number 1 and infinitely many $\mathbb{Q}$-rational points that is Zariski dense in the moduli space of K3 surfaces of degree 2. |
| title | Rational points on K3 surfaces of degree 2 |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.13262 |