Tropical curves of unibranch points and hypertangency
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917346117943296 |
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| author | Caporaso, Lucia Turchet, Amos |
| author_facet | Caporaso, Lucia Turchet, Amos |
| contents | We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of the curves at the contact point must be arithmetically related. A geometric condition: the tropical curves that we associate to the contact point must be isomorphic. Moreover, we prove closed formulas for the delta-invariant of a unibranch singularity, and for the dimension of the loci of curves with an assigned unibranch point. Our work is motivated by interest in the Lang exceptional set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17392 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical curves of unibranch points and hypertangency Caporaso, Lucia Turchet, Amos Algebraic Geometry 14H20, 14H50, 14T90 We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of the curves at the contact point must be arithmetically related. A geometric condition: the tropical curves that we associate to the contact point must be isomorphic. Moreover, we prove closed formulas for the delta-invariant of a unibranch singularity, and for the dimension of the loci of curves with an assigned unibranch point. Our work is motivated by interest in the Lang exceptional set. |
| title | Tropical curves of unibranch points and hypertangency |
| topic | Algebraic Geometry 14H20, 14H50, 14T90 |
| url | https://arxiv.org/abs/2406.17392 |