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Periods for rank 1 irregular singular connections on surfaces

Marco Hien
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Abstract

We define a period pairing for flat, irregular singular, rank one connections, satisfying a technical condition regarding its stationary set, on complex surfaces between de Rham cohomology of the connection and a modified singular homology, the rapid decay homology. We prove that this gives a perfect duality. A 2-dimensional version of confluent hypergeometrics are contructed as an example.

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Marco Hien. 2006-02-20. Periods for rank 1 irregular singular connections on surfaces. https://arxiv.org/abs/math/0505474

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