Asymptotic Behavior of Tropical Rank Functions
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911704015699968 |
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| author | Botero, Ana Maria Küronya, Alex Vital, Eduardo |
| author_facet | Botero, Ana Maria Küronya, Alex Vital, Eduardo |
| contents | We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and study tropical notions of volume associated to both divisors and tropical modules. We prove optimal asymptotic results for each case. In addition, we show that the tropical volume is compatible with the tropicalization of curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11166 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Behavior of Tropical Rank Functions Botero, Ana Maria Küronya, Alex Vital, Eduardo Algebraic Geometry Combinatorics 14Txx, 14H99, 14Hxx, 14C20, 14C40 We show that the asymptotic behavior of the two main competing notions of rank of a linear series on a tropical curve is governed by asymptotic invariants, closely paralleling the theory of volumes in algebraic geometry. We introduce and study tropical notions of volume associated to both divisors and tropical modules. We prove optimal asymptotic results for each case. In addition, we show that the tropical volume is compatible with the tropicalization of curves. |
| title | Asymptotic Behavior of Tropical Rank Functions |
| topic | Algebraic Geometry Combinatorics 14Txx, 14H99, 14Hxx, 14C20, 14C40 |
| url | https://arxiv.org/abs/2604.11166 |