## Coupled connections on a compact Riemann surface

- I. Biswas
- J. Math. Pures Appl
- 2003

- Published 2004

In the present paper, we study Appell’s differential equations, namely linear differential equations on a compact Riemann surface X, with analytic coefficients and regular singularities, whose solutions are everywhere meromorphic (cf. [Po], ch. V; an equation with regular singularities is also called “fuchsian”). In his work [Ap], Appell studies the differential equations of the first order, that correspond to the study of meromorphic connections with logaritmic poles on line bundles (cf. example 2.15). Vitali ([Vi1], [Vi2]) extends the analysis to higher orders, specially to the second order. In this paper, we study Appell’s differential equations using cohomological tecniques, following the line of Deligne ([De]) and Gunning ([Gu1]). The different tecnique allows to extend Vitali’s results. For a fixed Appell differential equation E, the analytic continuation

@inproceedings{Tovena2004FuchsianDE,
title={Fuchsian differential equations on Rie - mann surfaces with locally meromor - phic solutions},
author={Francesca Tovena},
year={2004}
}