On ramification divisors of functions in a punctured compact Riemann surface

P. Cutillas Ripoll
1989 Publicacions matemàtiques  
PASCUAL CUTILLAS RIPOLL 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 are studied 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 instante, 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
more » ... visor, it also has a finite divisor. It is also proved that for a given finite divisor 6 in V, the ramification divisors (with a fixed degree) of the functions of the said type whose divisor is 6, define a proper analytic subset of a certain symmetric power of V .
doi:10.5565/publmat_33189_14 fatcat:idta3kgomvbpba42tzz2r4yf3i