On ramifications divisors of functions in a punctured compact Riemann surface
- 1 Departamento de Matemáticas Universidad de Salamanca
ISSN: 0214-1493
Year of publication: 1989
Volume: 33
Issue: 1
Pages: 163-171
Type: Article
More publications in: Publicacions matematiques
Abstract
Let v be a compact Riemann surface and v' be the complement in v of a nonvoid finite subset. Let M(v') be the field of meromorphic functions in v'. In this paper we study the ramification divisors of the functions in M(v') which have exponential singularities of finite degree at the points of v-v', and one proves, for instance, that if a function in M(v') belongs to the subfield generated by the functions of this type, and has a finite ramification divisor, it also has a finite divisor. It is also proved that for a given finite divisor d in v', the ramification divisors (with a fixed degree) of the functions of the said type whose divisor id d, define a proper analytic subset of a certain symmetric power of v'.