On triple coverings of irrational curves

Kato, Takao; Keem, Changho; Ohbuchi, Akira

On triple coverings of irrational curves

Authors

Kato, Takao

Keem, Changho

Ohbuchi, Akira

Description

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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