标题： 关于曲线上线性系的Halphen理论 显示英文标题

标题： Towards a Halphen theory of linear series on curves

摘要： $P^3$ 中曲线 C 上的线性级数，当不包含被平面切割的级数时，即为“主级数”。 我们给出了这些级数的度数的下界，分别表示为 deg(C)、g(C) 和数 $s = min{i: h^0(I_C(i))\neq 0}$；作为推论，我们得到了 C 的角性 (gonality) 的界限。算例表明，我们的界限是严格的。 我们考虑了一般线性级数的情况以及高阶射影空间中曲线的情况的推广。 显示英文摘要

摘要： A linear series on a curve C in $P^3$ is "primary" when it does not contain the series cut by planes. We provide a lower bound for the degree of these series, in terms of deg(C), g(C) and of the number $s = min{i: h^0(I_C(i))\neq 0}$; as a corollary, we obtain bounds for the gonality of C. Examples show that our bound is sharp. Extensions to the case of general linear series and to the case of curves in higher projective spaces are considered.