Let ${\cal X}$ be a snc model of $X$. We define a map

$$i_{\cal X}:C_{\cal X}({\bf R})\to C_{X^{an}}({\bf R})$$

such as follows. For $J=\{j_{1},\dots,j_{k}\}\subset I_{\cal X}$ such that $D_{J}\neq\emptyset$ let us consider a point $x\in C_{\cal X}({\bf R})$

$$x=\sum_{i=1}^{k}a_{i}\langle D_{j_{i}}\rangle,\,\,\,a_{i}\in{{\bf R}}_{>0}\,\,\forall i\in\{1,\dots,k\}$$

and an affine Zariski open subset $U\subset{\cal X}$ containing the generic point of $D_{J}$. One can embed ${\cal O}(U)$ into the algebra of formal series $K_{J}[[z_{1},\dots,z_{k}]]$ where $K_{J}$ is the field of rational functions on $D_{J}$ and $z_{i}=0$ are equations of divisors $D_{j_{i}},\,\,i=1,\dots,k\,$. We define a valuation $v_{x}$ of ${\cal O}(U)$ by the formula

$$v_{x}\left(\sum_{n_{1},\dots,n_{k}\geq 0}c_{n_{1},\dots,n_{k}}\prod_{i=1}^{k}z_{i}^{n_{i}}\right)=\inf\left\{\sum a_{i}n_{i}\,|\,c_{n_{1},\dots,n_{k}}\neq 0\right\}\,\,.$$

We define $i_{\cal X}(x)$ to be the image of the point $v_{x}\in Spec^{an}({\cal O}(U)/K)$ in $X^{an}$. It is easy to check that the element $i_{\cal X}(x)$ does not depend on the choice of the open subset $U$.

The following proposition is obvious:

We will denote also by $i_{\cal X}$ the induced embedding $S_{\cal X}\hookrightarrow X^{an}$.