A compact Kähler manifold with semi-positive holomorphic sectional curvature is a locally trivial fibration over a finite étale quotient of a torus with rationally connected projective fibers.
Cao, Albanese maps of projective manifolds with nef anticanonical divisors, Ann
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Fundamental groups of compact K\"ahler manifolds with semi-positive holomorphic sectional curvature
A compact Kähler manifold with semi-positive holomorphic sectional curvature is a locally trivial fibration over a finite étale quotient of a torus with rationally connected projective fibers.