Projective bundles that admit coupled Kähler-Einstein metrics but no Kähler-Einstein metrics
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917290893639680 |
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| author | Yotsutani, Naoto |
| author_facet | Yotsutani, Naoto |
| contents | Using Hultgren's polytope formulation of the existence of coupled Kähler-Einstein (cKE) metrics on toric Fano manifolds, we construct explicit higher-dimensional toric Fano manifolds that admit two coupled Kähler-Einstein metrics but no ordinary Kähler-Einstein metrics. In particular, we exhibit such examples among certain projective bundles over products of projective spaces. Motivated by these constructions, we conjecture that examples of this type exist in all dimensions $n\geq 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Projective bundles that admit coupled Kähler-Einstein metrics but no Kähler-Einstein metrics Yotsutani, Naoto Differential Geometry Algebraic Geometry 14L24, 14M25, 53C55 Using Hultgren's polytope formulation of the existence of coupled Kähler-Einstein (cKE) metrics on toric Fano manifolds, we construct explicit higher-dimensional toric Fano manifolds that admit two coupled Kähler-Einstein metrics but no ordinary Kähler-Einstein metrics. In particular, we exhibit such examples among certain projective bundles over products of projective spaces. Motivated by these constructions, we conjecture that examples of this type exist in all dimensions $n\geq 4$. |
| title | Projective bundles that admit coupled Kähler-Einstein metrics but no Kähler-Einstein metrics |
| topic | Differential Geometry Algebraic Geometry 14L24, 14M25, 53C55 |
| url | https://arxiv.org/abs/2602.20488 |