Solution
= Solution
For a <projective scheme> $X$ of <dimension of a scheme> $n$ and a <Cartier divisor> $D$, <asymptotic Riemann–Roch> gives
$$
\boxed{\chi(X,\mathcal O_X(mD))=\frac{D^n}{n!}m^n+O(m^{n-1}).}
$$
Here <Euler characteristic of a coherent sheaf> means $\chi=\sum_{i=0}^n(-1)^ih^i$, and $D^n$ is the degree of the top <intersection product> with the fundamental cycle of $X$, including its component multiplicities. No <ampleness> assumption on $D$ is needed.