Betti structures of hypergeometric equations
Algebraic Geometry
2022-01-24 v3 Complex Variables
Abstract
We study Betti structures in the solution complexes of confluent hypergeometric equations. We use the framework of enhanced ind-sheaves and the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. The main result is a group theoretic criterion that ensures that enhanced solutions of such systems are defined over certain subfields of the complex numbers. The proof uses a description of the hypergeometric systems as exponentially twisted Gauss-Manin systems of certain Laurent polynomials.
Cite
@article{arxiv.2012.12140,
title = {Betti structures of hypergeometric equations},
author = {Davide Barco and Marco Hien and Andreas Hohl and Christian Sevenheck},
journal= {arXiv preprint arXiv:2012.12140},
year = {2022}
}