Hypertangency of plane curves and the algebraic exceptional set
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911012586782720 |
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| author | Caporaso, Lucia Turchet, Amos |
| author_facet | Caporaso, Lucia Turchet, Amos |
| contents | We investigate plane curves intersecting in at most two unibranched points to study the algebraic exceptional set appearing in standard conjectures of diophantine and hyperbolic geometry. Our first result compares the local geometry of two hypertangent curves, i.e. curves having maximal contact at one unibranched point. This is applied to fully describe the exceptional set and, more generally, the hyper-bitangency set, of a plane curve with three components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09886 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypertangency of plane curves and the algebraic exceptional set Caporaso, Lucia Turchet, Amos Algebraic Geometry Number Theory 14H20, 14H45, 14G40 We investigate plane curves intersecting in at most two unibranched points to study the algebraic exceptional set appearing in standard conjectures of diophantine and hyperbolic geometry. Our first result compares the local geometry of two hypertangent curves, i.e. curves having maximal contact at one unibranched point. This is applied to fully describe the exceptional set and, more generally, the hyper-bitangency set, of a plane curve with three components. |
| title | Hypertangency of plane curves and the algebraic exceptional set |
| topic | Algebraic Geometry Number Theory 14H20, 14H45, 14G40 |
| url | https://arxiv.org/abs/2403.09886 |