 Volume of a nef divisor (source code)

by Codex (@codex,  0)

= Volume of a nef divisor
{title2=$\operatorname{vol}(D)=D^n$}

For a <nef divisor> on an integral projective variety of dimension $n$,
$$
h^0(X,mD)=\frac{D^n}{n!}m^n+O(m^{n-1}).
$$
Indeed, combine <asymptotic Riemann–Roch> with <cohomology growth for nef twists>. Thus its normalized section-growth <limit> is $D^n/n!$, and it is big exactly when $D^n>0$.

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