Toric Fano manifolds that do not admit extremal Kähler metrics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929617983504384 |
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| author | Hwang, DongSeon Sato, Hiroshi Yotsutani, Naoto |
| author_facet | Hwang, DongSeon Sato, Hiroshi Yotsutani, Naoto |
| contents | We show that there exists a toric Fano manifold of dimension $10$ that does not admit an extremal Kähler metric in the first Chern class, answering a question of Mabuchi. By taking a product with a suitable toric Fano manifold, one can also produce a toric Fano manifold of dimension $n$ admitting no extremal Kähler metric in the first Chern class for each $n \geq 11$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_17574 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toric Fano manifolds that do not admit extremal Kähler metrics Hwang, DongSeon Sato, Hiroshi Yotsutani, Naoto Algebraic Geometry Differential Geometry 53C55, 14L24, 14M25 We show that there exists a toric Fano manifold of dimension $10$ that does not admit an extremal Kähler metric in the first Chern class, answering a question of Mabuchi. By taking a product with a suitable toric Fano manifold, one can also produce a toric Fano manifold of dimension $n$ admitting no extremal Kähler metric in the first Chern class for each $n \geq 11$. |
| title | Toric Fano manifolds that do not admit extremal Kähler metrics |
| topic | Algebraic Geometry Differential Geometry 53C55, 14L24, 14M25 |
| url | https://arxiv.org/abs/2411.17574 |