Counting rational points on Hirzebruch-Kleinschmidt varieties over number fields
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929439560957952 |
|---|---|
| author | Herrero, Sebastián Martínez, Tobías Montero, Pedro |
| author_facet | Herrero, Sebastián Martínez, Tobías Montero, Pedro |
| contents | We study the asymptotic growth of the number of rational points of bounded height on smooth projective split toric varieties with Picard rank 2 over number fields, with respect to Arakelov height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where explicit asymptotic formulas for the number of rational points of bounded height can be given. Additionally, we present various examples, including the case of Hirzebruch surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting rational points on Hirzebruch-Kleinschmidt varieties over number fields Herrero, Sebastián Martínez, Tobías Montero, Pedro Number Theory Algebraic Geometry 14G05, 14G40 (primary), 14G10, 14M25 (secondary) We study the asymptotic growth of the number of rational points of bounded height on smooth projective split toric varieties with Picard rank 2 over number fields, with respect to Arakelov height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where explicit asymptotic formulas for the number of rational points of bounded height can be given. Additionally, we present various examples, including the case of Hirzebruch surfaces. |
| title | Counting rational points on Hirzebruch-Kleinschmidt varieties over number fields |
| topic | Number Theory Algebraic Geometry 14G05, 14G40 (primary), 14G10, 14M25 (secondary) |
| url | https://arxiv.org/abs/2407.19408 |