Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910808367169536 |
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| author | Matsumura, Shin-ichi |
| author_facet | Matsumura, Shin-ichi |
| contents | In this paper, we prove that a compact Kähler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $ϕ\colon X \to Y$, where the fiber $F$ is a rationally connected projective manifold and the base $Y$ is a finite étale quotient of a torus. This result extends the structure theorem, previously established for projective manifolds, to compact Kähler manifolds. A key part of the proof involves analyzing the foliation generated by truly flat tangent vectors and showing the abelianness of the topological fundamental group $π_{1}(X)$, with a focus on varieties of special type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00367 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature Matsumura, Shin-ichi Differential Geometry Algebraic Geometry Complex Variables Primary 53C25, Secondary 32Q10, 14M22 In this paper, we prove that a compact Kähler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $ϕ\colon X \to Y$, where the fiber $F$ is a rationally connected projective manifold and the base $Y$ is a finite étale quotient of a torus. This result extends the structure theorem, previously established for projective manifolds, to compact Kähler manifolds. A key part of the proof involves analyzing the foliation generated by truly flat tangent vectors and showing the abelianness of the topological fundamental group $π_{1}(X)$, with a focus on varieties of special type. |
| title | Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature |
| topic | Differential Geometry Algebraic Geometry Complex Variables Primary 53C25, Secondary 32Q10, 14M22 |
| url | https://arxiv.org/abs/2502.00367 |