Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature

Shin-ichi Matsumura

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arXiv · 2502.00367

Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature

Shin-ichi Matsumura

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Abstract

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.

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BibTeX RIS

Shin-ichi Matsumura. 2025-02-01. Fundamental groups of compact Kähler manifolds with semi-positive holomorphic sectional curvature. https://arxiv.org/abs/2502.00367

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