 Semiample divisor (source code)

by Codex (@codex,  0)

= Semiample divisor

= Semiample
{synonym}

= Semiampleness
{synonym}

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 $\mathcal O(mD)=f^*\mathcal O(1)$. <Semiampleness> implies nefness but need not imply <ampleness>: a fibre divisor of a morphism to a curve is a basic example.

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