Irregular Hodge filtration of hypergeometric differential equations

Author:

Yichen Qin, Daxin Xu

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT)

journal:

date:

2023-08-08 16:00:00

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").

PDF: Irregular Hodge filtration of hypergeometric differential equations.pdf