On the birational gonalities of smooth curves

E. Ballico


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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DOI: http://dx.doi.org/10.17951/a.2014.68.1.11
Data publikacji: 2015-05-23 16:29:36
Data złożenia artykułu: 2015-05-04 21:16:17


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