Let X be a sufficiently general smooth k-gonal curve of genus g and R ∈ Pic(X) the degree k spanned line bundle. We find an optimal integer z > 0 such that the line bundle is very ample and projectively normal.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-5, author = {E. Ballico}, title = {Non-special projectively normal line bundles on general k-gonal curves}, journal = {Annales Polonici Mathematici}, volume = {83}, year = {2004}, pages = {55-60}, zbl = {1096.14500}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-5} }
E. Ballico. Non-special projectively normal line bundles on general k-gonal curves. Annales Polonici Mathematici, Tome 83 (2004) pp. 55-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap84-1-5/