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

Abstract

In this paper, we prove that a compact Kähler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $\varphi :X\to Y$, 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 ${\pi }_1(X)$, with a focus on varieties of special type.

19 pages, comments are welcome