Tropicalization of linear series and tilings by polymatroids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911869959143424 |
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| author | Amini, Omid Esteves, Eduardo |
| author_facet | Amini, Omid Esteves, Eduardo |
| contents | We show that tropicalization of linear series on curves gives rise to two-parameter families of tilings by polymatroids, with one parameter arising from the theory of divisors on tropical curves and the other from the reduction of linear series of rational functions in non-Archimedean geometry. In order to do this, we introduce a general framework that produces tilings of vector spaces and their subsets by polymatroids. We furthermore show that these tilings are regular and relate them to work by Kapranov and Lafforgue on Chow quotients of Grassmannians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropicalization of linear series and tilings by polymatroids Amini, Omid Esteves, Eduardo Algebraic Geometry Combinatorics Primary 14H10, 14T90, 14D06, 52C22. Secondary 05B45, 52B40 We show that tropicalization of linear series on curves gives rise to two-parameter families of tilings by polymatroids, with one parameter arising from the theory of divisors on tropical curves and the other from the reduction of linear series of rational functions in non-Archimedean geometry. In order to do this, we introduce a general framework that produces tilings of vector spaces and their subsets by polymatroids. We furthermore show that these tilings are regular and relate them to work by Kapranov and Lafforgue on Chow quotients of Grassmannians. |
| title | Tropicalization of linear series and tilings by polymatroids |
| topic | Algebraic Geometry Combinatorics Primary 14H10, 14T90, 14D06, 52C22. Secondary 05B45, 52B40 |
| url | https://arxiv.org/abs/2405.04306 |