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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.17237 |
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| _version_ | 1866916059846541312 |
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| author | Zhang, Shiyu |
| author_facet | Zhang, Shiyu |
| contents | We record two remarks. First, for a compact Kähler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact Kähler manifolds with quasi-negative $k$-Ricci curvature, $1<k<n$, or more generally with quasi-negative mixed curvature $C_{a,b}$ for $a,b>0$, the canonical bundle is ample. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17237 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature Zhang, Shiyu Differential Geometry We record two remarks. First, for a compact Kähler manifold with semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration is exactly the number of non-truly-flat directions. Second, for compact Kähler manifolds with quasi-negative $k$-Ricci curvature, $1<k<n$, or more generally with quasi-negative mixed curvature $C_{a,b}$ for $a,b>0$, the canonical bundle is ample. |
| title | Remark on semi-positive holomorphic sectional curvature and quasi-negative $k$-Ricci curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.17237 |