Constructions of superabundant tropical curves in higher genus
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910751641305088 |
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| author | Koyama, Sae |
| author_facet | Koyama, Sae |
| contents | We construct qualitatively new examples of superabundant tropical curves which are non-realizable in genus $3$ and $4$. These curves are in $\mathbb{R}^3$ and $\mathbb{R}^4$ respectively, and have properties resembling canonical embeddings of genus $3$ and $4$ algebraic curves. In particular, the genus $3$ example is a degree $4$ planar tropical curve, and the genus $4$ example is contained in the product of a tropical line and a tropical conic. They have excess dimension of deformation space equal to $1$. Non-realizability follows by combining this with a dimension calculation for the corresponding space of logarithmic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12538 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constructions of superabundant tropical curves in higher genus Koyama, Sae Algebraic Geometry We construct qualitatively new examples of superabundant tropical curves which are non-realizable in genus $3$ and $4$. These curves are in $\mathbb{R}^3$ and $\mathbb{R}^4$ respectively, and have properties resembling canonical embeddings of genus $3$ and $4$ algebraic curves. In particular, the genus $3$ example is a degree $4$ planar tropical curve, and the genus $4$ example is contained in the product of a tropical line and a tropical conic. They have excess dimension of deformation space equal to $1$. Non-realizability follows by combining this with a dimension calculation for the corresponding space of logarithmic curves. |
| title | Constructions of superabundant tropical curves in higher genus |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.12538 |