Primitive linear series on curves
Primitive linear series on curves
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曲线上的原始线性级数
DOI：
10.1007/bf02567056
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发表时间：
1992
影响因子：
0.6
通讯作者：
G. Martens
中科院分区：
文献类型：
--
作者：
M. Coppens;C. Keem;G. Martens
本文研究了曲线C的一个新的数值不变量，它与C上的本原线性级数有关。（下面定义的本原级数是C上的本质完备的特殊线性级数。对n ≤3的曲线进行了分类，并证明了对于给定的n，如果曲线的亏格足够高，则曲线是双覆盖的.主要工具是H. Martens-Mumford-型定理，并证明了这些定理的两个改进。
In this paper we study a new numerical invariant ℓ of curvesC which is related to the primitive linear series onC. (Primitive series—defined below—are the essential complete and special linear series onC.) The curves with ℓ≤3 are classified, and it is shown that for a given value of ℓ the curve is a double covering if its genus is sufficiently high. The main tool are dimension theorems of H. Martens-Mumford-type for the varieties of special divisors ofC, and we prove two refinements of these theorems.