On triple coverings of irrational curves
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 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 byexhibiting some examples.
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