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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.
Let C be a smooth integral projective curve admitting two pencils g
and g
such that g
+ g
is birational. We give conditions in order that the complete linear system |sg
+ rg
| be normally generated or very ample.
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