Integral points of bounded height on a certain toric variety
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866908365703086080 |
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| author | Wilsch, Florian |
| author_facet | Wilsch, Florian |
| contents | We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre's constant $α$ and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_10909 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Integral points of bounded height on a certain toric variety Wilsch, Florian Number Theory Algebraic Geometry 11D45 (Primary), 11G35, 14G05 (Secondary) We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre's constant $α$ and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties. |
| title | Integral points of bounded height on a certain toric variety |
| topic | Number Theory Algebraic Geometry 11D45 (Primary), 11G35, 14G05 (Secondary) |
| url | https://arxiv.org/abs/2202.10909 |