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arXiv · 2012.12140

Betti structures of hypergeometric equations

Davide Barco·Marco Hien·Andreas Hohl·Christian Sevenheck
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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.

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Davide Barco, Marco Hien, Andreas Hohl, Christian Sevenheck. 2020-12-22. Betti structures of hypergeometric equations. https://arxiv.org/abs/2012.12140

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