On the birational gonalities of smooth curves

E. Ballico

doi:10.2478/umcsmath-2014-0002

On the birational gonalities of smooth curves

E. Ballico

Abstract

Let

$C$ be a smooth curve of genus

$g$ . For each positive integer

$r$ the birational

$r$ -gonality

$s_r(C)$ of

$C$ is the minimal integer

$t$ such that there is

$L\in \mbox{Pic}^t(C)$ with

$h^0(C,L) =r+1$ . Fix an integer

$r\ge 3$ . In this paper we prove the existence of an integer

$g_r$ such that for every integer

$g\ge g_r$ there is a smooth curve

$C$ of genus

$g$ with

$s_{r+1}(C)/(r+1) > s_r(C)/r$ , i.e. in the sequence of all birational gonalities of

$C$ at least one of the slope inequalities fails.

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References

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DOI: http://dx.doi.org/10.2478/umcsmath-2014-0002
Date of publication: 2015-05-23 16:29:36
Date of submission: 2015-05-04 21:16:17

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