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Projectivity criteria for K\"ahler morphisms
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In this short note we prove two projectivity criteria for fibrations between mildly singular compact K\"ahler spaces. They are the relative versions of the celebrated criteria of Kodaira and Moishezon. As an application we obtain that the MRC fibration always has a model that is a projective morphism.
Forward citations
Cited by 3 Pith papers
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On the K\"ahler MMP and the transcendental base-point-free theorem
Big gklt Kähler pairs admit a full MMP with scaling, and a nef canonical class with modified-big boundary is semiample (Tosatti’s conjecture).
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Compact K\"ahler manifolds with nef anti-canonical bundle
Every compact Kähler manifold with nef anti-canonical bundle admits a locally trivial fibration over a Calabi-Yau manifold with rationally connected fibers.
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On compact K\"ahler manifolds with pseudo-effective tangent bundle
Compact Kähler manifolds with pseudo-effective tangent bundle admit a smooth fibration whose base is an étale quotient of a torus and whose fibers are rationally connected.
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