Big divisor
= Big divisor
= Big Cartier divisor
{synonym}
A <Cartier divisor> $D$ on an integral $n$-dimensional projective variety is big when $h^0(X,mD)\geq c m^n$ for some $c>0$ and infinitely many positive integers $m$. Equivalently, its <Iitaka dimension> is $n$. <Kodaira's lemma> characterizes bigness by an ample-plus-effective decomposition, and the <birational linear system criterion for bigness> shows why this growth captures the full variety.