Finitely generated congruences on tropical rational function semifields
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911884837388288 |
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| author | Song, JuAe |
| author_facet | Song, JuAe |
| contents | We prove that the congruence on the tropical rational function semifield in $n$-variables associated with a subset $V$ of $\boldsymbol{R}^n$ is finitely generated if and only if the closure of $V$ is a finite union of $\boldsymbol{R}$-rational polyhedral sets. With this fact, we characterize rational function semifields of tropical curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14087 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finitely generated congruences on tropical rational function semifields Song, JuAe Algebraic Geometry 14T10, 14T15, 14T20, 14T25, 15A80 We prove that the congruence on the tropical rational function semifield in $n$-variables associated with a subset $V$ of $\boldsymbol{R}^n$ is finitely generated if and only if the closure of $V$ is a finite union of $\boldsymbol{R}$-rational polyhedral sets. With this fact, we characterize rational function semifields of tropical curves. |
| title | Finitely generated congruences on tropical rational function semifields |
| topic | Algebraic Geometry 14T10, 14T15, 14T20, 14T25, 15A80 |
| url | https://arxiv.org/abs/2405.14087 |