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arXiv · 2505.07685

Periods of fibre products of elliptic surfaces and the Gamma conjecture

Eric Pichon-Pharabod
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Abstract

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.

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Eric Pichon-Pharabod. 2025-05-12. Periods of fibre products of elliptic surfaces and the Gamma conjecture. https://arxiv.org/abs/2505.07685

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