Isomorphisms between certain function fields over compact Riemann surfaces (Q1067043)

Let \({\mathcal V}\) be a compact Riemann surface and let \({\mathcal M}({\mathcal V})\) be the field of meromorphic functions on \({\mathcal V}\). If \(S_ 1\) and \(S_ 2\) are nonempty finite subsets of \({\mathcal V}\), it is proved in this paper that there exists an isomorphism between the fields generated over \({\mathcal M}({\mathcal V})\) by all meromorphic functions having a finite divisor on \({\mathcal V}-S_ 1\) and \({\mathcal V}-S_ 2\) respectively, whose restriction to \({\mathcal M}({\mathcal V})\) is the identity mapping. This kind of isomorphism is also characterized in various ways.