Singular K\"ahler-Einstein metrics and RCD spaces

G\'abor Sz\'ekelyhidi

Singular K\"ahler-Einstein metrics and RCD spaces

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arxiv 2408.10747 v2 pith:C3G7TMA3 submitted 2024-08-20 math.DG

Singular K\"ahler-Einstein metrics and RCD spaces

G\'abor Sz\'ekelyhidi This is my paper

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keywords metricsahler-einsteinsingularapproximationcompletionconstantcurvaturehomeomorphic

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We study K\"ahler-Einstein metrics on singular projective varieties. We show that under an approximation property with constant scalar curvature metrics, the metric completion of the smooth part is a non-collapsed RCD space, and is homeomorphic to the original variety.

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Ricci-flat metrics on Calabi-Yau manifolds
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A survey of the degeneration theory of Ricci-flat Kahler metrics on Calabi-Yau manifolds: smooth limits for semiample and nef-and-big classes, path-dependent counterexamples at the boundary, and a list of open conjectures.