Let C be a smooth curve of genus g. For each positive integer r the r-gonality d r (C) of C is the minimal integer t such that there is L Î Pict(C){Lin {rm Pic}^t(C)} with h 0(C, L) = r + 1. Here we use nodal plane curves to construct several smooth curves C with d 2(C)/2 < d 3(C)/3, i.e., for which a slope inequality fails.
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机译：令C为g族的光滑曲线。对于每个正整数r，C的r角d r （C）是最小整数t，使得存在LÎPic t （C）{Lin {rm Pic} ^ t（C）}的h 0 （C，L）= r +1。在这里，我们使用节点平面曲线构造了多个具有d 2 的平滑曲线C （C）/ 2 3 （C）/ 3，即斜率不等式失效。
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