Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916274774212608 |
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| author | Dasgupta, Jyoti Gangopadhyay, Chandranandan Kaveh, Kiumars Manon, Christopher |
| author_facet | Dasgupta, Jyoti Gangopadhyay, Chandranandan Kaveh, Kiumars Manon, Christopher |
| contents | We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-Süss on one hand, and Klyachko's classification of equivariant vector bundles on toric varieties on the other hand. A main ingredient in our classification is the classification of torus equivariant vector bundles on toric schemes over a DVR in terms of piecewise affine maps to the (extended) Bruhat-Tits building of the general linear group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings Dasgupta, Jyoti Gangopadhyay, Chandranandan Kaveh, Kiumars Manon, Christopher Algebraic Geometry 14L30 (primary), 20E42 (secondary) We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-Süss on one hand, and Klyachko's classification of equivariant vector bundles on toric varieties on the other hand. A main ingredient in our classification is the classification of torus equivariant vector bundles on toric schemes over a DVR in terms of piecewise affine maps to the (extended) Bruhat-Tits building of the general linear group. |
| title | Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings |
| topic | Algebraic Geometry 14L30 (primary), 20E42 (secondary) |
| url | https://arxiv.org/abs/2406.02912 |