Let $\mathcal{X}$ be any SNC model of $X$.

• (i)

  The image of the evaluation map $\ev_{\mathcal{X}}:X\to\Div_{0}(\mathcal{X})^{*}_{\mathbf{R}}$ coincides with $\Delta_{\mathcal{X}}$.

• (ii)

  There exists a unique continuous (injective) map $\emb_{\mathcal{X}}:\Delta_{\mathcal{X}}\to X$ such that:

  • (a)

    $\ev_{\mathcal{X}}\circ\emb_{\mathcal{X}}$ is the identity on $\Delta_{\mathcal{X}}$;

  • (b)

    for $s\in\Delta_{\mathcal{X}}$, the center of $\emb_{\mathcal{X}}(s)$ on $\mathcal{X}$ is the generic point $\xi_{J}$ of $E_{J}$ for the unique subset $J\subset I$ such that $s$ is contained in the relative interior of $\sigma_{J}$.