Remarks on Singular K\"ahler-Einstein Metrics
Differential Geometry
2025-05-06 v1
Abstract
We study two different natural notions of singular K\"ahler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat K\"ahler cone metrics that arise as non-collapsed limits of sequences of K\"ahler-Einstein metrics or K\"ahler-Ricci flows, we show that an a priori weaker notion is equivalent to the stronger one introduced by Eyssidieux-Guedj-Zeriahi, and in particular the underlying variety has log terminal singularities in this case. Our method applies to more general singular K\"ahler-Einstein spaces as well, assuming that they define RCD spaces.
Cite
@article{arxiv.2505.01943,
title = {Remarks on Singular K\"ahler-Einstein Metrics},
author = {Max Hallgren and Gábor Székelyhidi},
journal= {arXiv preprint arXiv:2505.01943},
year = {2025}
}
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18 pages