Let "X" be a projective variety over a field "k". Then multiplying a global section of "O"("D") by a nonzero scalar in "k" does not change its zero locus. As a result, the projective space of lines in the "k"-vector space of global sections "H"0("X", "O"("D")) can be identified with the set of effective divisors linearly equivalent to "D", called the complete linear system of "D". A projective linear subspace of this projective space is called a linear system of divisors.