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arXiv · 2308.05138

Irregular Hodge filtration of hypergeometric differential equations

Yichen Qin·Daxin Xu
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Abstract

Fedorov and Sabbah--Yu calculated the (irregular) Hodge numbers of hypergeometric connections. In this paper, we study the irregular Hodge filtrations on hypergeometric connections defined by rational parameters, and provide a new proof of the aforementioned results. Our approach is based on a geometric interpretation of hypergeometric connections, which enables us to show that certain hypergeometric sums are everywhere ordinary on $|\mathbb{G}_{m,\mathbb{F}_p}|$ (i.e. "Frobenius Newton polygon equals to irregular Hodge polygon").

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Yichen Qin, Daxin Xu. 2023-08-09. Irregular Hodge filtration of hypergeometric differential equations. https://doi.org/10.2140/ant.2025.19.2481

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