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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.11530 |
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| _version_ | 1866915212330795008 |
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| author | Müller, Niklas |
| author_facet | Müller, Niklas |
| contents | Up to finite étale cover, any smooth complex projective variety $X$ with nef anti-canonical bundle is a holomorphic fibre bundle over a $K$-trivial variety with locally constant transition functions. We show that this result is optimal by proving that any projective fibre bundle with locally constant transition functions over a $K$-trivial variety has a nef anti-canonical bundle. Moreover, we complement some results on the structure theory of varieties whose tangent bundle admits a singular hermitean metric of positive curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_11530 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Locally Constant Fibrations and Positivity of Curvature Müller, Niklas Algebraic Geometry Up to finite étale cover, any smooth complex projective variety $X$ with nef anti-canonical bundle is a holomorphic fibre bundle over a $K$-trivial variety with locally constant transition functions. We show that this result is optimal by proving that any projective fibre bundle with locally constant transition functions over a $K$-trivial variety has a nef anti-canonical bundle. Moreover, we complement some results on the structure theory of varieties whose tangent bundle admits a singular hermitean metric of positive curvature. |
| title | Locally Constant Fibrations and Positivity of Curvature |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2212.11530 |