Remark 19.7.37219FB2B3C530

Remark 19.7.37.219FB2B3C530 The construction of $\Delta $ is independent of the choice of $C$ in the following sense. If $C'$ is another cone satisfying the same assumptions as $C$ and $C'\supseteq C$, then the Okounkov body map $\Delta \colon \overline{\mathcal{S}'(C')}_{>0}\rightarrow \mathcal{K}_ n$ extends the corresponding map (19.7.33). We will use this fact without further comment.