Double covering of curves

Ballico, Edoardo; Keem, Changho; Park, Seungsuk

doi:10.1090/S0002-9939-04-07426-X

Double covering of curves
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by Edoardo Ballico, Changho Keem and Seungsuk Park PDF

Proc. Amer. Math. Soc. 132 (2004), 3153-3158 Request permission

Abstract:

Let $C$ be a smooth projective algebraic curve of genus $q$ and $g$ an integer with $g\ge 4q+5$. For all integers $d\ge g-2q+1$ we prove the existence of a double covering $f:X\to C$ with $X$ a smooth curve of genus $g$ and the existence of a degree $d$ morphism $u:X\to \mathbb P^1$ that does not factor through $f$. By the Castelnuovo-Severi inequality, the result is sharp (except perhaps the bound $g\ge 4q+5$).

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