Singular Kähler metrics with Ricci curvature bounded below and rational cohomology class induce non-collapsed RCD spaces homeomorphic to the projective variety, under a resolution condition on the anti-canonical bundle.
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Nash entropy, Calabi energy and geometric regularization of singular K\"ahler metrics
Singular Kähler metrics with Ricci curvature bounded below and rational cohomology class induce non-collapsed RCD spaces homeomorphic to the projective variety, under a resolution condition on the anti-canonical bundle.