Toric models of smooth Fano threefolds
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913428915879936 |
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| author | Loginov, Konstantin Moraga, Joaquín Vasilkov, Artem |
| author_facet | Loginov, Konstantin Moraga, Joaquín Vasilkov, Artem |
| contents | We prove that a general rational smooth Fano threefold admits a toric model. More precisely, for a general rational smooth Fano threefold $X$, we show the existence of a boundary divisor $D$ for which $(X,D)\simeq_{\rm cbir} (\mathbb{P}^3,H_0+H_1+H_2+H_3)$, where the $H_i$'s are the coordinate hyperplanes. In particular, a general rational smooth Fano threefold has birational complexity zero. We argue that the three conditions: rationality, generality, and smoothness are indeed necessary for the theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toric models of smooth Fano threefolds Loginov, Konstantin Moraga, Joaquín Vasilkov, Artem Algebraic Geometry Primary 14B05, 14E30, 14L24, 14M25, Secondary 14A20, 53D20 We prove that a general rational smooth Fano threefold admits a toric model. More precisely, for a general rational smooth Fano threefold $X$, we show the existence of a boundary divisor $D$ for which $(X,D)\simeq_{\rm cbir} (\mathbb{P}^3,H_0+H_1+H_2+H_3)$, where the $H_i$'s are the coordinate hyperplanes. In particular, a general rational smooth Fano threefold has birational complexity zero. We argue that the three conditions: rationality, generality, and smoothness are indeed necessary for the theorem. |
| title | Toric models of smooth Fano threefolds |
| topic | Algebraic Geometry Primary 14B05, 14E30, 14L24, 14M25, Secondary 14A20, 53D20 |
| url | https://arxiv.org/abs/2407.09420 |