We find some ranges for the 4-tuples of integers (d,g,n,r) for which there is a smooth connected non-degenerate curve of degree d and genus g, which is k-normal for every k ≤ r.
@article{urn:eudml:doc:44345, title = {On the existence of k-normal curves of given degree and genus in projective spaces.}, journal = {Collectanea Mathematica}, volume = {55}, year = {2004}, pages = {269-277}, zbl = {1075.14028}, mrnumber = {MR2099218}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44345} }
Ballico, Edoardo; Chiarli, N.; Greco, S. On the existence of k-normal curves of given degree and genus in projective spaces.. Collectanea Mathematica, Tome 55 (2004) pp. 269-277. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44345/