Points of bounded height on quintic del Pezzo surfaces over number fields
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909803104698368 |
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| author | Bernert, Christian Derenthal, Ulrich |
| author_facet | Bernert, Christian Derenthal, Ulrich |
| contents | We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to universal torsors, we first show that we may restrict the torsor variables to their typical sizes, and then we can solve the counting problem in the framework of o-minimal structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Points of bounded height on quintic del Pezzo surfaces over number fields Bernert, Christian Derenthal, Ulrich Number Theory Algebraic Geometry 11G35 (Primary) 11D45, 14G05 (Secondary) We prove Manin's conjecture for split smooth quintic del Pezzo surfaces over arbitrary number fields with respect to fairly general anticanonical height functions. After passing to universal torsors, we first show that we may restrict the torsor variables to their typical sizes, and then we can solve the counting problem in the framework of o-minimal structures. |
| title | Points of bounded height on quintic del Pezzo surfaces over number fields |
| topic | Number Theory Algebraic Geometry 11G35 (Primary) 11D45, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2405.20293 |