光滑曲线的双族性

E. Ballico
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引用次数: 1

摘要

设\(C\)为\(g\)属的光滑曲线。对于每一个正整数\(r\), \(C\)的双方\(r\) -共向性\(s_r(C)\)是最小整数\(t\),使得\(L\in \mbox{Pic}^t(C)\)与\(h^0(C,L) =r+1\)存在交集。修复一个整数\(r\ge 3\)。本文证明了一个整数\(g_r\)的存在性,使得对于每一个整数\(g\ge g_r\)都存在一条具有\(s_{r+1}(C)/(r+1) > s_r(C)/r\)的属\(g\)的光滑曲线\(C\),即在\(C\)的所有双族共向性序列中至少有一个斜率不等式不成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the birational gonalities of smooth curves
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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