Birational complexity and conic fibrations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912928667533312 |
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| author | Moraga, Joaquín |
| author_facet | Moraga, Joaquín |
| contents | Let $(X,B)$ be a log Calabi-Yau pair of dimension $n$, index one, and birational complexity $c$. We show that $(X,B)$ has a crepant birational model that admits a tower of Mori fiber spaces of which at least $n-c$ are conic fibrations. Motivated by the proof of the previous statement, we introduce new measures of the complexity of a log Calabi-Yau pair; the alteration complexity and the conic complexity. We characterize when these invariants are zero. Finally, we give applications of the tools of the main theorem to birational superrigidity, Fano hypersurfaces, dual complexes, Weil indices of Fano varieties, and klt singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Birational complexity and conic fibrations Moraga, Joaquín Algebraic Geometry Primary 14E05, 14E30, Secondary 14D06 Let $(X,B)$ be a log Calabi-Yau pair of dimension $n$, index one, and birational complexity $c$. We show that $(X,B)$ has a crepant birational model that admits a tower of Mori fiber spaces of which at least $n-c$ are conic fibrations. Motivated by the proof of the previous statement, we introduce new measures of the complexity of a log Calabi-Yau pair; the alteration complexity and the conic complexity. We characterize when these invariants are zero. Finally, we give applications of the tools of the main theorem to birational superrigidity, Fano hypersurfaces, dual complexes, Weil indices of Fano varieties, and klt singularities. |
| title | Birational complexity and conic fibrations |
| topic | Algebraic Geometry Primary 14E05, 14E30, Secondary 14D06 |
| url | https://arxiv.org/abs/2403.17251 |