Log Calabi-Yau pairs of birational complexity zero
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916197926174720 |
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| author | Enwright, Joshua Figueroa, Fernando Moraga, Joaquín |
| author_facet | Enwright, Joshua Figueroa, Fernando Moraga, Joaquín |
| contents | In this article, we study the geometry of log Calabi-Yau pairs $(X,B)$ of index one and birational complexity zero. Firstly, we propose a conjecture that characterizes such pairs $(X,B)$ in terms of their dual complex and the rationality of their log canonical places. Secondly, we show that for these pairs the open set $X\setminus B$ is divisorially covered by open affine subvarieties which are isomorphic to open subvarieties of algebraic tori. We introduce and study invariants that measure the geometry and the number of these open subvarieties of algebraic tori. Thirdly, we study boundedness properties of log Calabi-Yau pairs of index one and birational complexity zero. For instance, in dimension $2$ we prove that such pairs are affinely bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05878 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log Calabi-Yau pairs of birational complexity zero Enwright, Joshua Figueroa, Fernando Moraga, Joaquín Algebraic Geometry 14E05, 14J32, 14E30 In this article, we study the geometry of log Calabi-Yau pairs $(X,B)$ of index one and birational complexity zero. Firstly, we propose a conjecture that characterizes such pairs $(X,B)$ in terms of their dual complex and the rationality of their log canonical places. Secondly, we show that for these pairs the open set $X\setminus B$ is divisorially covered by open affine subvarieties which are isomorphic to open subvarieties of algebraic tori. We introduce and study invariants that measure the geometry and the number of these open subvarieties of algebraic tori. Thirdly, we study boundedness properties of log Calabi-Yau pairs of index one and birational complexity zero. For instance, in dimension $2$ we prove that such pairs are affinely bounded. |
| title | Log Calabi-Yau pairs of birational complexity zero |
| topic | Algebraic Geometry 14E05, 14J32, 14E30 |
| url | https://arxiv.org/abs/2404.05878 |