= Class-group generator of a well-formed weighted projective space
{title2=$[F_i]=q_iH$}
The <toric divisor class sequence> identifies the <divisor class group> with $\mathbb Z$ via $(a_i)\mapsto\sum q_ia_i$. Choose integers $a_i$ with $\sum q_ia_i=1$; then $D=\sum a_iF_i$ represents its positive generator $H$. This is an ample <Q-Cartier divisor>: for $\ell=\operatorname{lcm}(q_i)$ the local Cartier data of $\ell D$ on the chart omitting ray $j$ is $m_j=(\ell/q_j)e_j-\ell(a_i)$, which satisfies the strict <toric ampleness criterion>. The generator need not itself be a <Cartier divisor>; for example the positive generator on $\mathbb P(1,1,2)$ has Cartier index two.
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