If the dual Kähler cone of a compact Kähler manifold contains a rational class as an interior point, then its Albanese variety is projective.
Bimeromorphic geometry of K\"ahler threefolds
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abstract
We describe the recently established minimal model program for (non-algebraic) K\"ahler threefolds as well as the abundance theorem for these spaces.
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2020 1verdicts
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On the dual positive cones and the algebraicity of a compact K\"ahler manifold
If the dual Kähler cone of a compact Kähler manifold contains a rational class as an interior point, then its Albanese variety is projective.