Periods of fibre products of elliptic surfaces and the Gamma conjecture
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912470921117696 |
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| author | Pichon-Pharabod, Eric |
| author_facet | Pichon-Pharabod, Eric |
| contents | We provide an algorithm for computing a basis of homology of fibre products of elliptic surfaces over $\mathbb P^1$, along with the corresponding intersection product and period matrices. We use this data to investigate the Gamma conjecture for Calabi-Yau threefolds obtained in this manner. We find a formula that works for all operators of a list of 105 fibre products, as well as for fourth order operators of the Calabi-Yau database. This algorithm comes with a SageMath implementation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periods of fibre products of elliptic surfaces and the Gamma conjecture Pichon-Pharabod, Eric Algebraic Geometry Symbolic Computation 14Q15, 14J32, 32G20 (Primary) 14D05, 14J33 (Secondary) We provide an algorithm for computing a basis of homology of fibre products of elliptic surfaces over $\mathbb P^1$, along with the corresponding intersection product and period matrices. We use this data to investigate the Gamma conjecture for Calabi-Yau threefolds obtained in this manner. We find a formula that works for all operators of a list of 105 fibre products, as well as for fourth order operators of the Calabi-Yau database. This algorithm comes with a SageMath implementation. |
| title | Periods of fibre products of elliptic surfaces and the Gamma conjecture |
| topic | Algebraic Geometry Symbolic Computation 14Q15, 14J32, 32G20 (Primary) 14D05, 14J33 (Secondary) |
| url | https://arxiv.org/abs/2505.07685 |