Kähler-Einstein toric submanifolds of the projective space
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918229763424256 |
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| author | Di Scala, Antonio J. Sombra, Martín |
| author_facet | Di Scala, Antonio J. Sombra, Martín |
| contents | We show that the Kähler-Einstein metrics on the four families of examples of symmetric toric Fano manifolds presented by Batyrev and Selivanova cannot be realized as metrics induced by immersions into projective spaces equipped with Fubini-Study metrics. We obtain a similar conclusion for the non-symmetric examples discovered by Nill and Paffenholz. A consequence is that a centrally symmetric toric Fano manifold admits a Kähler-Einstein metric induced by a projective immersion if and only if it is a product of projective lines. These results provide evidence for a broader conjecture characterizing which Kähler-Einstein metrics can be induced by projective immersions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kähler-Einstein toric submanifolds of the projective space Di Scala, Antonio J. Sombra, Martín Differential Geometry Algebraic Geometry Combinatorics Primary 53C55, Secondary 14M25, 32Q20, 53C24 We show that the Kähler-Einstein metrics on the four families of examples of symmetric toric Fano manifolds presented by Batyrev and Selivanova cannot be realized as metrics induced by immersions into projective spaces equipped with Fubini-Study metrics. We obtain a similar conclusion for the non-symmetric examples discovered by Nill and Paffenholz. A consequence is that a centrally symmetric toric Fano manifold admits a Kähler-Einstein metric induced by a projective immersion if and only if it is a product of projective lines. These results provide evidence for a broader conjecture characterizing which Kähler-Einstein metrics can be induced by projective immersions. |
| title | Kähler-Einstein toric submanifolds of the projective space |
| topic | Differential Geometry Algebraic Geometry Combinatorics Primary 53C55, Secondary 14M25, 32Q20, 53C24 |
| url | https://arxiv.org/abs/2512.03617 |