Base point free pencils on multiple coverings of smooth curves

Abstract

Abstract. Fix an integer k ≥ 2 and a smooth genus q projective curve X. Here we prove the existence of a smooth curve C, a degree k morphism C → X and a low degree base point free linear system on C not coming from X. Mathematics Subject Classification: 14H51; 14H30Keywords: multiple coverings of curves; base point free pencilsWe will follow the notations of [2] and [3] concerning ruled surfaces over a smooth projective curve X. If S := P(O X ⊕ R), R ∈ Pic(X), deg(R) ≤ 0, we will write X 0 (resp. X 1 ) for the unisecant divisor of the ruling S → X associated to the projection of O X ⊕ R onto the first (resp. second) factors. Thus X