Fuchsian differential equations on Rie - mann surfaces with locally meromor - phic solutions

  • Francesca Tovena
  • Published 2004

Abstract

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

Cite this paper

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