A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909680921477120 |
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| author | Birkar, Caucher Lee, Seung-Joo |
| author_facet | Birkar, Caucher Lee, Seung-Joo |
| contents | We compute an explicit rank bound on the Picard group of the compact surfaces, which can serve as the base of an elliptic Calabi-Yau variety with canonical singularities. To bound the Picard rank from above, we develop a novel strategy in birational geometry, motivated in part by the physics of six-dimensional vacua of F-theory as discussed in a companion paper [1] to this one. The derivation of the concrete bound illustrates the strategy and clarifies the origin of the boundedness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds Birkar, Caucher Lee, Seung-Joo High Energy Physics - Theory Algebraic Geometry We compute an explicit rank bound on the Picard group of the compact surfaces, which can serve as the base of an elliptic Calabi-Yau variety with canonical singularities. To bound the Picard rank from above, we develop a novel strategy in birational geometry, motivated in part by the physics of six-dimensional vacua of F-theory as discussed in a companion paper [1] to this one. The derivation of the concrete bound illustrates the strategy and clarifies the origin of the boundedness. |
| title | A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2507.06317 |