Parabolic vector bundles and Lie algebroid connections
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911372917342208 |
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| author | Alfaya, David Biswas, Indranil Kumar, Pradip Singh, Anoop |
| author_facet | Alfaya, David Biswas, Indranil Kumar, Pradip Singh, Anoop |
| contents | Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure over the marked points. An analogue of the Atiyah exact sequence for parabolic Lie algebroids is constructed. For any Lie algebroid whose underlying holomorphic vector bundle is stable, we give a complete characterization of all the parabolic vector bundles that admit a parabolic Lie algebroid connection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15828 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parabolic vector bundles and Lie algebroid connections Alfaya, David Biswas, Indranil Kumar, Pradip Singh, Anoop Algebraic Geometry Differential Geometry 14H60 (Primary) 53B15, 70G45 (Secondary) Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure over the marked points. An analogue of the Atiyah exact sequence for parabolic Lie algebroids is constructed. For any Lie algebroid whose underlying holomorphic vector bundle is stable, we give a complete characterization of all the parabolic vector bundles that admit a parabolic Lie algebroid connection. |
| title | Parabolic vector bundles and Lie algebroid connections |
| topic | Algebraic Geometry Differential Geometry 14H60 (Primary) 53B15, 70G45 (Secondary) |
| url | https://arxiv.org/abs/2406.15828 |