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On triple coverings of irrational curves

Takao Kato·Changho Keem·Akira Ohbuchi
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Abstract

Given a triple covering $X$ of genus $g$ of a general (in the sense of Brill-Noether) curve $C$ of genus $h$, we show the existence of base-point-free pencils of degree $d$ which are not composed with the triple covering for any $d\ge g-[{3h+1\over 2}]-1$ by utilizing some enumerative methods and computations. We also discuss about the sharpness of our main result and the so-called Castelnuovo-Severi bound byexhibiting some examples.

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Takao Kato, Changho Keem, Akira Ohbuchi. 1995-07-05. On triple coverings of irrational curves. https://arxiv.org/abs/alg-geom/9506026

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