Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910238797463552 |
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| author | Chen, Qile Lehmann, Brian Tanimoto, Sho |
| author_facet | Chen, Qile Lehmann, Brian Tanimoto, Sho |
| contents | We explore log Manin's conjecture for integral points and its connections to $\mathbb A^1$-connectedness. We prove log Manin's conjecture for Campana rational curves and for $\mathbb A^1$-curves on split toric varieties. Our arguments combine the Cox ring description of the moduli space of rational curves with Batyrev's heuristic-type counting arguments. As our proofs are geometric in nature, they give a geometric explanation of the mysterious leading constant for Campana points proposed by Chow--Loughran--Takloo-Bighash--Tanimoto. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19898 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness Chen, Qile Lehmann, Brian Tanimoto, Sho Algebraic Geometry Number Theory We explore log Manin's conjecture for integral points and its connections to $\mathbb A^1$-connectedness. We prove log Manin's conjecture for Campana rational curves and for $\mathbb A^1$-curves on split toric varieties. Our arguments combine the Cox ring description of the moduli space of rational curves with Batyrev's heuristic-type counting arguments. As our proofs are geometric in nature, they give a geometric explanation of the mysterious leading constant for Campana points proposed by Chow--Loughran--Takloo-Bighash--Tanimoto. |
| title | Manin's conjecture for semi-integral curves and $\mathbb A^1$-connectedness |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2605.19898 |