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 $f:X\to Y$ where $Y$ is a smooth algebraic curve. In this paper, we investigate the existence of morphisms from $X$ to the projective line ${\mathbf{P}}^1$ 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.

23 pages, 1 figure