An abundance-type result for the tangent bundles of smooth Fano varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912744434827264 |
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| author | Wang, Juanyong |
| author_facet | Wang, Juanyong |
| contents | In this paper we prove the following abundance-type result: for any smooth Fano variety $X$, the tangent bundle $T_X$ is nef if and only if it is big and semiample in the sense that the tautological line bundle $\mathscr{O}_{\mathbb{P}T_X}(1)$ is so, by which we establish a weak form of the Campana-Peternell conjecture (Camapan-Peternell, 1991). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03799 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An abundance-type result for the tangent bundles of smooth Fano varieties Wang, Juanyong Algebraic Geometry 14J45, 14E30, 14M17, 32J27 In this paper we prove the following abundance-type result: for any smooth Fano variety $X$, the tangent bundle $T_X$ is nef if and only if it is big and semiample in the sense that the tautological line bundle $\mathscr{O}_{\mathbb{P}T_X}(1)$ is so, by which we establish a weak form of the Campana-Peternell conjecture (Camapan-Peternell, 1991). |
| title | An abundance-type result for the tangent bundles of smooth Fano varieties |
| topic | Algebraic Geometry 14J45, 14E30, 14M17, 32J27 |
| url | https://arxiv.org/abs/2408.03799 |