Remarks on Singular Kähler-Einstein Metrics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912360527036416 |
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| author | Hallgren, Max Székelyhidi, Gábor |
| author_facet | Hallgren, Max Székelyhidi, Gábor |
| contents | We study two different natural notions of singular Kähler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat Kähler cone metrics that arise as non-collapsed limits of sequences of Kähler-Einstein metrics or Kähler-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 Kähler-Einstein spaces as well, assuming that they define RCD spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on Singular Kähler-Einstein Metrics Hallgren, Max Székelyhidi, Gábor Differential Geometry We study two different natural notions of singular Kähler-Einstein metrics on normal complex varieties. In the setting of singular Ricci flat Kähler cone metrics that arise as non-collapsed limits of sequences of Kähler-Einstein metrics or Kähler-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 Kähler-Einstein spaces as well, assuming that they define RCD spaces. |
| title | Remarks on Singular Kähler-Einstein Metrics |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.01943 |