International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 2, Pages 397-402
doi:10.1155/S0161171284000405
The Serre duality theorem for Reimann surfaces
Department of Mathematics, Beloit College, Beloit 53511, Wisconsin, USA
Received 29 January 1984
Copyright © 1984 Ranjan Roy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.