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The Miyaoka-Yau inequality on smooth minimal models
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In this short note, we offer an observation that the Miyaoka-Yau inequality holds for any compact K\"{a}hler manifold with nef canonical bundle, i.e. a smooth minimal model. It follows directly from the existence of cscK metrics in a neighborhood of the canonical class which was confirmed both by the work of Dyrefelt and Song using different approaches.
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Classification of Smooth Minimal K\"ahler Fourfolds Without Effective Divisors and Surfaces
Compact Kähler fourfolds with pseudo-effective K_X and no codimension-1 or -2 subvarieties have torsion K_X, hence are torus quotients or IHS manifolds.
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