BASE-POINT-FREE PENCILS ON TRIPLE COVERS OF SMOOTH CURVES

Abstract

Let X be a smooth algebraic curve. Suppose that there exists a triple covering f: X → Y where Y is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from X to the projective line P1 which do not factor through the covering f. For this purpose, we generalize the classical results of Maroni concerning base-point-free pencils on trigonal curves to the case of triple covers of arbitrary smooth irrational curves.