 Complete linear system of a divisor

This is the full linear system of divisors, obtained by using every global section of the associated line bundle. For a Cartier divisor on an integral projective variety, the complete linear system $|D|$ consists of its effective representatives under linear equivalence of Cartier divisors. A basis of $H^0(X,{\mathcal{O}}_X(D))$ defines a rational map to projective space.