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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06933 |
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| _version_ | 1866915415096033280 |
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| author | Jun, Jaiung Mincheva, Kalina Tolliver, Jeffrey |
| author_facet | Jun, Jaiung Mincheva, Kalina Tolliver, Jeffrey |
| contents | We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group $\text{Pic}_G(X)$. Finally, we prove a version of Klyachko's classification theorem for toric vector bundles over an idempotent semifield. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant vector bundles on toric schemes over semirings Jun, Jaiung Mincheva, Kalina Tolliver, Jeffrey Algebraic Geometry 14A23, 14T10, 14C22 We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme $X$ over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group $\text{Pic}_G(X)$. Finally, we prove a version of Klyachko's classification theorem for toric vector bundles over an idempotent semifield. |
| title | Equivariant vector bundles on toric schemes over semirings |
| topic | Algebraic Geometry 14A23, 14T10, 14C22 |
| url | https://arxiv.org/abs/2406.06933 |