One reason to study the space of global sections of a line bundle is to understand the possible maps from a given variety to projective space. This is essential for the classification of algebraic varieties. Explicitly, a morphism from a variety "X" to projective space P"n" over a field "k" determines a line bundle "L" on "X", the pullback of the standard line bundle "O"(1) on P"n". Moreover, "L" comes with "n"+1 sections whose base locus (the intersection of their zero sets) is empty. Conversely, any line bundle "L" with "n"+1 global sections whose common base locus is empty determines a morphism "X" → P"n". These observations lead to several notions of positivity for Cartier divisors (or line bundles), such as ample divisors and nef divisors.