On compact Kähler manifolds with pseudo-effective tangent bundle
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913674111746048 |
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| author | Matsumura, Shin-ichi Qing, Chenghao |
| author_facet | Matsumura, Shin-ichi Qing, Chenghao |
| contents | In this paper, we prove that a compact Kähler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $ϕ\colon X \to Y$ onto a finite étale quotient $Y$ of a compact complex torus. This result extends the structure theorem previously established for smooth projective varieties to compact Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On compact Kähler manifolds with pseudo-effective tangent bundle Matsumura, Shin-ichi Qing, Chenghao Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 14F35, 58A30 In this paper, we prove that a compact Kähler manifold $X$ with pseudo-effective (resp. singular positively curved) tangent bundle admits a smooth (resp. locally constant) rationally connected fibration $ϕ\colon X \to Y$ onto a finite étale quotient $Y$ of a compact complex torus. This result extends the structure theorem previously established for smooth projective varieties to compact Kähler manifolds. |
| title | On compact Kähler manifolds with pseudo-effective tangent bundle |
| topic | Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 14F35, 58A30 |
| url | https://arxiv.org/abs/2502.00623 |