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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02569 |
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| _version_ | 1866909766873251840 |
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| author | Dodwell, Emily |
| author_facet | Dodwell, Emily |
| contents | We formulate and prove an analogue of the balancing condition for the tropicalization of a curve in a torus bundle $X$. We find that the usual balancing condition fails when the bundle is non-trivial and that the failure is captured by the first Chern classes of the line bundles associated to $X$. We discuss a geometric perspective of tropicalization where the weights arise naturally from intersection theory. The relations between divisors on a toric variety bundle put constraints on these weights which leads to the balancing condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical geometry in torus bundles Dodwell, Emily Algebraic Geometry We formulate and prove an analogue of the balancing condition for the tropicalization of a curve in a torus bundle $X$. We find that the usual balancing condition fails when the bundle is non-trivial and that the failure is captured by the first Chern classes of the line bundles associated to $X$. We discuss a geometric perspective of tropicalization where the weights arise naturally from intersection theory. The relations between divisors on a toric variety bundle put constraints on these weights which leads to the balancing condition. |
| title | Tropical geometry in torus bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.02569 |