PomeDefinition 19.4.2.0F5DB984097B We will write
\[ \begin{aligned} \Gamma (\theta ,\varphi )\coloneqq & \left\{ (\nu (s),k) : k\in \mathbb {N}, s\in \mathrm{H}^0(X,L^ k\otimes \mathcal{I}(k\varphi ))^{\times } \right\} ,\\ \Delta _ k(\theta ,\varphi )\coloneqq & \mathrm{Conv}\left\{ k^{-1}\nu (s): s\in \mathrm{H}^0\left(X,L^ k\otimes \mathcal{I}(k\varphi )\right)^{\times } \right\} \subseteq \mathbb {R}^ n, \end{aligned} \]
where the second set is defined only for those $k$ such that $\mathrm{H}^0(X,L^ k\otimes \mathcal{I}(k\varphi ))\neq 0$.
When $\varphi =V_{\theta }$, we simply write $\Gamma (L)$ and $\Delta _ k(L)$ instead.
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