Abstract: | 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 ({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. |