Bounds on the Mordell-Weil rank of elliptic fibrations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911545045286912 |
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| author | Grassi, Antonella Miranda, Rick Paranjape, Kapil Srinivas, Vasudevan Weigand, Timo |
| author_facet | Grassi, Antonella Miranda, Rick Paranjape, Kapil Srinivas, Vasudevan Weigand, Timo |
| contents | We present two proofs for a bound on the rank of the Mordell-Weil group of some elliptic fibrations. The bounds apply to Calabi-Yau varieties, which are also of interest to the physics of string theory. We prove explicit bounds for Calabi-Yau threefolds, as predicted by physics, and give new explicit bounds for fourfolds under mild assumptions. These results motivate a conjecture for bounds in any dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounds on the Mordell-Weil rank of elliptic fibrations Grassi, Antonella Miranda, Rick Paranjape, Kapil Srinivas, Vasudevan Weigand, Timo Algebraic Geometry High Energy Physics - Theory We present two proofs for a bound on the rank of the Mordell-Weil group of some elliptic fibrations. The bounds apply to Calabi-Yau varieties, which are also of interest to the physics of string theory. We prove explicit bounds for Calabi-Yau threefolds, as predicted by physics, and give new explicit bounds for fourfolds under mild assumptions. These results motivate a conjecture for bounds in any dimensions. |
| title | Bounds on the Mordell-Weil rank of elliptic fibrations |
| topic | Algebraic Geometry High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.24666 |