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 $d\geq g-[(3h+1)/2]-1$ by utilizing some enumerative methods and computations. We also discuss about the sharpness of our main result and the so-called Castelnuovo-Severi bound by exhibiting some examples.
Citation
Takao Kato. Changho Keem. Akira Ohbuchi. "On triple coverings of irrational curves." Tsukuba J. Math. 21 (2) 421 - 441, October 1997. https://doi.org/10.21099/tkbjm/1496163250
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