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arXiv · 0806.1849

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

Dongsoo Shin
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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.

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Dongsoo Shin. 2008-06-11. Base-point-free pencils on triple covers of smooth curves. https://arxiv.org/abs/0806.1849

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