Base-point-free pencils on triple covers of smooth curves

Details Base-point-free pencils on triple covers of smooth curves Base-point-free pencils on triple covers of smooth curves

2008-06-11

arxiv.org/abs/0806.1849v1

International Journal of Mathematics 19 (2008), no. 6, 1--27

Mathematics

Algebraic Geometry

23 pages, 1 figure

Scientific paper

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.

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