A compact Kähler manifold is uniruled exactly when its canonical line bundle is not pseudoeffective, proved by carrying Bost's algebraicity criterion to the Kähler setting.
The pseudo-effective cone of a compact K \"ahler manifold and varieties of negative K odaira dimension
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A characterization of uniruled compact K\"ahler manifolds
A compact Kähler manifold is uniruled exactly when its canonical line bundle is not pseudoeffective, proved by carrying Bost's algebraicity criterion to the Kähler setting.