Interpolation of low degree points on curves
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909724903997440 |
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| author | Granot, Eden |
| author_facet | Granot, Eden |
| contents | We study points of moderately low degree on a curve $C$ over a number field, which is embedded on a nice toric surface $S$. Recently, Smith and Vogt related the linear equivalence classes of such points to intersections of $C$ with curves in the ambient surface. We show that when $C$ is sufficiently effective and ample with simple singularities, all but finitely many sufficiently low degree points are obtained via intersections of $C$ with curves in the ambient surface $S$. Our methods make use of the toric geometry of the ambient surface $S$ to produce curves which interpolate the low degree points on $C$. Furthermore, we generalise a result by Debarre and Klassen to singular plane curves and higher degrees of points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04426 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpolation of low degree points on curves Granot, Eden Algebraic Geometry Number Theory We study points of moderately low degree on a curve $C$ over a number field, which is embedded on a nice toric surface $S$. Recently, Smith and Vogt related the linear equivalence classes of such points to intersections of $C$ with curves in the ambient surface. We show that when $C$ is sufficiently effective and ample with simple singularities, all but finitely many sufficiently low degree points are obtained via intersections of $C$ with curves in the ambient surface $S$. Our methods make use of the toric geometry of the ambient surface $S$ to produce curves which interpolate the low degree points on $C$. Furthermore, we generalise a result by Debarre and Klassen to singular plane curves and higher degrees of points. |
| title | Interpolation of low degree points on curves |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2508.04426 |