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

Pascual Cutillas Ripoll

Publicacions Matemàtiques (1989)

  • Volume: 33, Issue: 1, page 163-171
  • ISSN: 0214-1493

Abstract

top
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'.

How to cite

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.