We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the curve.
@article{urn:eudml:doc:44321, title = {Curves on a smooth quadric.}, journal = {Collectanea Mathematica}, volume = {54}, year = {2003}, pages = {309-325}, zbl = {1048.14014}, mrnumber = {MR2010792}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44321} }
Giuffrida, S.; Maggioni, R. Curves on a smooth quadric.. Collectanea Mathematica, Tome 54 (2003) pp. 309-325. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44321/