 Semiample divisor

A Cartier divisor is semiample if some positive multiple is a basepoint-free divisor, equivalently its divisor line bundle has a globally generated positive power. Such a power defines a Kodaira map $f$ with $\mathcal{O}(mD)=f^{\ast }\mathcal{O}(1)$. Semiampleness implies nefness but need not imply ampleness: a fibre divisor of a morphism to a curve is a basic example.