A canonicity criterion for toric varieties and the classification of canonical 4-simplices
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912977660149760 |
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| author | Ghirlanda, Marco |
| author_facet | Ghirlanda, Marco |
| contents | Based on the Reid-Shepherd-Barron-Tai criterion for canonical and terminal quotient singularities, we characterize canonicity and terminality of a toric variety in terms of its local class group actions. Specializing it to the Picard number one setting, we arrive at a classification algorithm for canonical and terminal fake weighted projective spaces in any dimension. In dimension four it gives, up to isomorphism, 710450 canonical fake weighted projective spaces. We take a look at the corresponding Calabi-Yau hypersurfaces, compute the Fine interior of the associated canonical simplices, and discuss the results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_21198 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A canonicity criterion for toric varieties and the classification of canonical 4-simplices Ghirlanda, Marco Algebraic Geometry Combinatorics 14M25, 52B20, 14J32 Based on the Reid-Shepherd-Barron-Tai criterion for canonical and terminal quotient singularities, we characterize canonicity and terminality of a toric variety in terms of its local class group actions. Specializing it to the Picard number one setting, we arrive at a classification algorithm for canonical and terminal fake weighted projective spaces in any dimension. In dimension four it gives, up to isomorphism, 710450 canonical fake weighted projective spaces. We take a look at the corresponding Calabi-Yau hypersurfaces, compute the Fine interior of the associated canonical simplices, and discuss the results. |
| title | A canonicity criterion for toric varieties and the classification of canonical 4-simplices |
| topic | Algebraic Geometry Combinatorics 14M25, 52B20, 14J32 |
| url | https://arxiv.org/abs/2603.21198 |