Abstract
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.
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