2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122136Let X be a smooth curve of genus g. When pi>=3g and d>=pi-2g+1 we show the existence of a double covering gamma:C-->X where C a smooth curve of genus pi with a base-point-free pencil of degree d which is not the pull-back of a pencil on X.Algebraic Geometry14H51; 14H30text