Let C be a smooth 5-gonal curve of genus 9. Assume all linear systems g1 5 on C are of type I (i.e. they can be counted with multiplicity 1) and let m be the numer of linear systems g1 5 on C. The only possibilities are m=1; m=2; m=3 and m=6. Each of those possibilities occur.
@article{urn:eudml:doc:41818,
title = {Five-gonal curves of genus nine.},
journal = {Collectanea Mathematica},
volume = {56},
year = {2005},
pages = {21-26},
zbl = {1066.14034},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41818}
}
Coppens, Marc. Five-gonal curves of genus nine.. Collectanea Mathematica, Tome 56 (2005) pp. 21-26. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41818/