Compact Kähler manifolds with nef anti-canonical bundle
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913917492527104 |
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| author | Matsumura, Shin-ichi Wang, Juanyong Wu, Xiaojun Zhang, Qimin |
| author_facet | Matsumura, Shin-ichi Wang, Juanyong Wu, Xiaojun Zhang, Qimin |
| contents | In this paper, we prove that a compact Kähler manifold $X$ with the nef anti-canonical bundle $-K_{X}$ admits a locally trivial fibration $ϕ\colon X \to Y$, where the fiber $F$ is a rationally connected manifold and the base $Y$ is a Calabi--Yau manifold. We introduce a suitable approach that extends the strategy of Cao--Höring, originally developed for smooth projective varieties, to more general singular Kähler spaces. A key technical ingredient is a flatness criterion for pseudo-effective sheaves with vanishing first Chern class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compact Kähler manifolds with nef anti-canonical bundle Matsumura, Shin-ichi Wang, Juanyong Wu, Xiaojun Zhang, Qimin Algebraic Geometry Complex Variables Differential Geometry Primary 32Q30, Secondary 14C30, 14E30 In this paper, we prove that a compact Kähler manifold $X$ with the nef anti-canonical bundle $-K_{X}$ admits a locally trivial fibration $ϕ\colon X \to Y$, where the fiber $F$ is a rationally connected manifold and the base $Y$ is a Calabi--Yau manifold. We introduce a suitable approach that extends the strategy of Cao--Höring, originally developed for smooth projective varieties, to more general singular Kähler spaces. A key technical ingredient is a flatness criterion for pseudo-effective sheaves with vanishing first Chern class. |
| title | Compact Kähler manifolds with nef anti-canonical bundle |
| topic | Algebraic Geometry Complex Variables Differential Geometry Primary 32Q30, Secondary 14C30, 14E30 |
| url | https://arxiv.org/abs/2506.23218 |