Projectively Normal Embedding of a k -Gonal Curve#

Abstract

Let C be a k-gonal curve with a simple pencil |F| of degree k. First we show that if C has a complete for , then = || + B for some , where B is the base locus of . Using this, || = and K(−) is very ample for any if . Also we prove that K(−) is normally generated if is simple and (respectively ) for k ≥ 7 (respectively 4 ≤ k ≤ 6).