A canonical Fano threefold has Fano index $\leq 66$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909858314321920 |
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| author | Jiang, Chen Liu, Haidong |
| author_facet | Jiang, Chen Liu, Haidong |
| contents | We show that the $\mathbb{Q}$-Fano index of a canonical weak Fano $3$-fold is at most $66$. This upper bound is optimal and gives an affirmative answer to a conjecture of Chengxi Wang in dimension $3$. During the proof, we establish a new Riemmann--Roch formula for canonical $3$-folds and provide a detailed study of non-isolated singularities on canonical Fano $3$-folds, concerning both their local and global properties. Our proof also involves a Kawamata--Miyaoka type inequality and geometry of foliations of rank $2$ on canonical Fano $3$-folds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A canonical Fano threefold has Fano index $\leq 66$ Jiang, Chen Liu, Haidong Algebraic Geometry Primary 14J45, Secondary 14J30, 14J10, 14E30, 14C20, 14C40 We show that the $\mathbb{Q}$-Fano index of a canonical weak Fano $3$-fold is at most $66$. This upper bound is optimal and gives an affirmative answer to a conjecture of Chengxi Wang in dimension $3$. During the proof, we establish a new Riemmann--Roch formula for canonical $3$-folds and provide a detailed study of non-isolated singularities on canonical Fano $3$-folds, concerning both their local and global properties. Our proof also involves a Kawamata--Miyaoka type inequality and geometry of foliations of rank $2$ on canonical Fano $3$-folds. |
| title | A canonical Fano threefold has Fano index $\leq 66$ |
| topic | Algebraic Geometry Primary 14J45, Secondary 14J30, 14J10, 14E30, 14C20, 14C40 |
| url | https://arxiv.org/abs/2508.16364 |