Tropical Vector Bundles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913342787944448 |
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| author | Khan, Bivas Maclagan, Diane |
| author_facet | Khan, Bivas Maclagan, Diane |
| contents | The goal of this paper is to introduce a construction of a vector bundle on a tropical variety. When the base is a tropical toric variety these tropicalize toric vector bundles, and are described by the data of a valuated matroid and some flats in the lattice of flats of the underlying matroid. The fibers are tropical linear spaces. We define global sections for tropical toric vector bundles, stability, and Jordan-Hölder and Harder-Narasimhan filtrations. Many of these require additional modularity assumptions on the defining matroid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03505 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tropical Vector Bundles Khan, Bivas Maclagan, Diane Algebraic Geometry Combinatorics The goal of this paper is to introduce a construction of a vector bundle on a tropical variety. When the base is a tropical toric variety these tropicalize toric vector bundles, and are described by the data of a valuated matroid and some flats in the lattice of flats of the underlying matroid. The fibers are tropical linear spaces. We define global sections for tropical toric vector bundles, stability, and Jordan-Hölder and Harder-Narasimhan filtrations. Many of these require additional modularity assumptions on the defining matroid. |
| title | Tropical Vector Bundles |
| topic | Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2405.03505 |