International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 397-402
doi:10.1155/S0161171284000405

The Serre duality theorem for Riemann surfaces

Abstract

Given a Riemann surface S, there exists a finitely generated Fuchsian group G of the first kind acting on the upper half plane U, such that S≅U/G. This isomorphism makes it possible to use Fuchsian group methods to prove theorems about Riemann surfaces. In this note we give a proof of the Serre duality theorem by Fuchsian group methods which is technically simpler than proofs depending on sheaf theoretic methods.