On ramifications divisors of functions in a punctured compact Riemann surface.

Cutillas Ripoll, Pascual. "On ramifications divisors of functions in a punctured compact Riemann surface.." Publicacions Matemàtiques 33.1 (1989): 163-171. <http://eudml.org/doc/41077>.

@article{CutillasRipoll1989,
abstract = {Let ν be a compact Riemann surface and ν' be the complement in ν of a nonvoid finite subset. Let M(ν') be the field of meromorphic functions in ν'. In this paper we study the ramification divisors of the functions in M(ν') which have exponential singularities of finite degree at the points of ν-ν', and one proves, for instance, that if a function in M(ν') 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 δ in ν', the ramification divisors (with a fixed degree) of the functions of the said type whose divisor id δ, define a proper analytic subset of a certain symmetric power of ν'.},
author = {Cutillas Ripoll, Pascual},
journal = {Publicacions Matemàtiques},
keywords = {Superficies Riemann; Divisores; Función meromorfa; ramification; function field; divisors},
language = {eng},
number = {1},
pages = {163-171},
title = {On ramifications divisors of functions in a punctured compact Riemann surface.},
url = {http://eudml.org/doc/41077},
volume = {33},
year = {1989},
}

TY - JOUR
AU - Cutillas Ripoll, Pascual
TI - On ramifications divisors of functions in a punctured compact Riemann surface.
JO - Publicacions Matemàtiques
PY - 1989
VL - 33
IS - 1
SP - 163
EP - 171
AB - Let ν be a compact Riemann surface and ν' be the complement in ν of a nonvoid finite subset. Let M(ν') be the field of meromorphic functions in ν'. In this paper we study the ramification divisors of the functions in M(ν') which have exponential singularities of finite degree at the points of ν-ν', and one proves, for instance, that if a function in M(ν') 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 δ in ν', the ramification divisors (with a fixed degree) of the functions of the said type whose divisor id δ, define a proper analytic subset of a certain symmetric power of ν'.
LA - eng
KW - Superficies Riemann; Divisores; Función meromorfa; ramification; function field; divisors
UR - http://eudml.org/doc/41077
ER -