Holomorphic Lie algebroid connections over rationally connected varieties
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917540167417856 |
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| author | Biswas, Indranil Singh, Anoop |
| author_facet | Biswas, Indranil Singh, Anoop |
| contents | Take a holomorphic Lie algebroid $(V,ϕ)$ over a rationally connected smooth complex projective variety $X$. We show that, under certain conditions, a vector bundle $E$ over $X$ admits a $(V,ϕ)$-connection if and only if $E$ is trivial. Moreover, we prove that under the same conditions, any $(V,ϕ)$-connection over $X$ is flat. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28256 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holomorphic Lie algebroid connections over rationally connected varieties Biswas, Indranil Singh, Anoop Algebraic Geometry Take a holomorphic Lie algebroid $(V,ϕ)$ over a rationally connected smooth complex projective variety $X$. We show that, under certain conditions, a vector bundle $E$ over $X$ admits a $(V,ϕ)$-connection if and only if $E$ is trivial. Moreover, we prove that under the same conditions, any $(V,ϕ)$-connection over $X$ is flat. |
| title | Holomorphic Lie algebroid connections over rationally connected varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.28256 |