Periods for rank 1 irregular singular connections on surfaces

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.Comment: 28 pages; previous version partly incorrect (for higher rank case), new version contains case of line bundles and a new example. v3: technical assumption inserted (Definition 1.1

Stokes matrices for confluent hypergeometric equations

We apply the method of [arXiv:1705.07610] to compute the Stokes matrices of non-resonant confluent hypergeometric differential equations. We discuss the ambiguity of the presentation of the Stokes matrices regarding different choices. The results rely on an explicit description of the perverse sheaf associated to the non-confluent regular singular hypergeometric system arising via Fourier-Laplace transform. We give assumptions on the parameter such that the Stokes matrices have rational or real values. Under some more restrictive conditions, the Stokes matrices had been computed by Duval-Mitschi before. We compare our results with their formulae in the unramified case.Comment: 34 pages, 5 figures v4: section on the ramified case added, will be published in International Mathematics Research Notice