On coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914547750666240 |
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| author | Futaki, Akito |
| author_facet | Futaki, Akito |
| contents | We consider coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds. These are natural generalizations of Kähler-Einstein metrics. As in the case of Kähler-Einstein metrics, the existence is known to be equivalent to algebraic conditions which generalize the K-polystability. In this survey, we outline recent developments for these two cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08789 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds Futaki, Akito Differential Geometry Algebraic Geometry 14J45, 32G05, 32Q15, 53C55 We consider coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds. These are natural generalizations of Kähler-Einstein metrics. As in the case of Kähler-Einstein metrics, the existence is known to be equivalent to algebraic conditions which generalize the K-polystability. In this survey, we outline recent developments for these two cases. |
| title | On coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds |
| topic | Differential Geometry Algebraic Geometry 14J45, 32G05, 32Q15, 53C55 |
| url | https://arxiv.org/abs/2605.08789 |