Remarks on Singular K\"ahler-Einstein Metrics

Max Hallgren; Gábor Székelyhidi

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arXiv · 2505.01943

Remarks on Singular K\"ahler-Einstein Metrics

Max Hallgren·Gábor Székelyhidi

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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.

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Max Hallgren, Gábor Székelyhidi. 2025-05-03. Remarks on Singular K\"ahler-Einstein Metrics. https://arxiv.org/abs/2505.01943

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