Singular K\"ahler-Einstein metrics and RCD spaces
G\'abor Sz\'ekelyhidi
TL;DR
This paper investigates the relationship between singular Kähler-Einstein metrics on projective varieties and RCD spaces, demonstrating that under certain approximation conditions, the metric completion aligns with the original variety and forms a non-collapsed RCD space.
Contribution
It establishes that the metric completion of the smooth part of a singular Kähler-Einstein variety is a non-collapsed RCD space homeomorphic to the original variety under approximation conditions.
Findings
The metric completion of the smooth part is a non-collapsed RCD space.
The completion is homeomorphic to the original variety.
Results connect singular Kähler-Einstein metrics with RCD space theory.
Abstract
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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Taxonomy
TopicsAdvanced Differential Geometry Research · Geometry and complex manifolds · Geometric Analysis and Curvature Flows