Exceptional Fano 3-folds from rational curves
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917274536902656 |
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| author | Valle, Jaime Cuadros Vicente, Joe Lope |
| author_facet | Valle, Jaime Cuadros Vicente, Joe Lope |
| contents | We show exceptionality of certain families of non-quasismooth weighted hypersurfaces. In particular these admit Kähler-Einstein metrics. Our examples are produced by the monomials generating the complex deformations of orbifolds whose corresponding $S^1$-Seifert bundles are smooth rational homology 7-spheres admitting Sasaki-Einstein metrics. From our construction, it follows that these exceptional Fano hypersurfaces describe elements in the boundary of the K-moduli of $\mathbb{Q}$-Fano 3-folds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exceptional Fano 3-folds from rational curves Valle, Jaime Cuadros Vicente, Joe Lope Algebraic Geometry 14B05, 14J30, 14J45, 32Q20 We show exceptionality of certain families of non-quasismooth weighted hypersurfaces. In particular these admit Kähler-Einstein metrics. Our examples are produced by the monomials generating the complex deformations of orbifolds whose corresponding $S^1$-Seifert bundles are smooth rational homology 7-spheres admitting Sasaki-Einstein metrics. From our construction, it follows that these exceptional Fano hypersurfaces describe elements in the boundary of the K-moduli of $\mathbb{Q}$-Fano 3-folds. |
| title | Exceptional Fano 3-folds from rational curves |
| topic | Algebraic Geometry 14B05, 14J30, 14J45, 32Q20 |
| url | https://arxiv.org/abs/2602.13487 |