For a closed subvariety $Y$ of $T$ of dimension $n$, the tropical variety associated to $X$ is defined by ${\rm Trop}(Y):={{\rm trop}}({Y^{\rm an}})$. The Bieri–Groves theorem says that ${\rm Trop}(Y)$ is a finite union of $n$-dimensional integral $\Gamma$-affine polyhedra in ${\mathbb{R}}^{r}$. It is shown in tropical geometry that ${\rm Trop}(Y)$ is an integral $\Gamma$-affine polyhedral complex. The polyhedral structure is only determined up to subdivision which does not matter for our constructions. We will see below that the tropical variety is endowed with a positive canonical weight $m$ satisfying the balancing condition from 3.7. We get a tropical cycle of pure dimension $n$ which we also denote by ${\rm Trop}(Y)$ forgetting the weight $m$ in the notation.