The complement of tropical curves in moderate position on tropical surfaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911818547462144 |
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| author | Tsutsui, Yuki |
| author_facet | Tsutsui, Yuki |
| contents | López de Medrano, Rincón and Shaw defined the Chern classes on tropical manifolds as an extension of their theory of the Chern-Schwartz-MacPherson cycles on matroids. This makes it possible to define the Riemann-Roch number of tropical Cartier divisors on compact tropical manifolds. In this paper, we introduce the notion of a moderate position, and discuss a conjecture that the Riemann-Roch number $\operatorname{RR}(X;D)$ of a tropical submanifold $D$ of codimension $1$ in moderate position on a compact tropical manifold $X$ is equal to the topological Euler characteristic of the complement $X\setminus D$. In particular, we prove it and its generalization when $\dim X=2$ and $X$ admits a Delzant face structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The complement of tropical curves in moderate position on tropical surfaces Tsutsui, Yuki Algebraic Geometry López de Medrano, Rincón and Shaw defined the Chern classes on tropical manifolds as an extension of their theory of the Chern-Schwartz-MacPherson cycles on matroids. This makes it possible to define the Riemann-Roch number of tropical Cartier divisors on compact tropical manifolds. In this paper, we introduce the notion of a moderate position, and discuss a conjecture that the Riemann-Roch number $\operatorname{RR}(X;D)$ of a tropical submanifold $D$ of codimension $1$ in moderate position on a compact tropical manifold $X$ is equal to the topological Euler characteristic of the complement $X\setminus D$. In particular, we prove it and its generalization when $\dim X=2$ and $X$ admits a Delzant face structure. |
| title | The complement of tropical curves in moderate position on tropical surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.19576 |