Isomorphisms between certain function fields over compact Riemann surfaces
type: Item
instance of: scholarly article
title: Isomorphisms between certain function fields over compact Riemann surfaces
zbMATH Open document ID: 0579.30043
DOI: 10.1007/BF01458585
author: Pascual Cutillas Ripoll
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164135
review text: 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.
Mathematics Subject Classification ID: 30F10
zbMATH DE Number: 3927322
zbMATH Keywords: field of meromorphic functions
MaRDI profile type: Publication
cites work: Construction of Certain Function Fields Associated with a Compact Riemann Surface
cites work: Q3931656
cites work: Some Picard Theorems for Holomorphic Maps to Algebraic Varieties
cites work: Lectures on Riemann Surfaces: Jacobi Varieties
cites work: Q5666814
description: scientific article; zbMATH DE number 3927322